Classify angles worksheet for Grade 8 students, featuring exercises on complementary, supplementary, and adjacent angles with diagrams and problems to solve.

Let's solve each problem step by step, based on the image you provided.

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1.

Given: Two angles forming a straight line: 120° and $ x^\circ $

- These are supplementary (they form a straight line = 180°).
- So:
$$
120^\circ + x = 180^\circ \Rightarrow x = 60^\circ
$$

✔ Answer: Supplementary, $ x = 60^\circ $

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2.

Given: Two intersecting lines with one angle labeled $ 119^\circ $, and opposite angle $ x^\circ $

- Opposite angles formed by intersecting lines are vertical angles, so they are equal.
- So:
$$
x = 119^\circ
$$

✔ Answer: Vertical angles (not supplementary or adjacent), $ x = 119^\circ $

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3.

Given: A right angle split into two parts: $ x^\circ $ and $ 55^\circ $

- Right angle = $ 90^\circ $
- So:
$$
x + 55^\circ = 90^\circ \Rightarrow x = 35^\circ
$$

✔ Answer: Complementary (sum to 90°), $ x = 35^\circ $

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4.

Given: An angle of $ 40^\circ $ and $ x^\circ $ forming a straight line

- Straight line → supplementary angles
- So:
$$
40^\circ + x = 180^\circ \Rightarrow x = 140^\circ
$$

✔ Answer: Supplementary, $ x = 140^\circ $

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5.

Given: A right angle ($ 90^\circ $) and an angle of $ 80^\circ $, and $ x^\circ $ is the remaining part

- The total angle at the vertex is $ 90^\circ $, and $ 80^\circ $ is one part.
- So:
$$
x = 90^\circ - 80^\circ = 10^\circ
$$

✔ Answer: Complementary (since they add up to 90°), $ x = 10^\circ $

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6.

Given: A straight line with $ 98^\circ $ and $ x^\circ $

- These form a straight line → supplementary
- So:
$$
98^\circ + x = 180^\circ \Rightarrow x = 82^\circ
$$

✔ Answer: Supplementary, $ x = 82^\circ $

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7.

Given: A right angle (90°), with one angle $ 22^\circ $, and $ x^\circ $ is the other part

- So:
$$
x + 22^\circ = 90^\circ \Rightarrow x = 68^\circ
$$

✔ Answer: Complementary, $ x = 68^\circ $

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8.

Given: Two intersecting lines, one angle is $ 59^\circ $, and $ x^\circ $ is vertical to it

- Vertical angles are equal → $ x = 59^\circ $

✔ Answer: Vertical angles, $ x = 59^\circ $

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9.

Given: A straight line with two angles: $ x^\circ $ and $ 6^\circ $, but they are on a straight line

- So:
$$
x + 6^\circ = 180^\circ \Rightarrow x = 174^\circ
$$

✔ Answer: Supplementary, $ x = 174^\circ $

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10.

Given: A transversal crossing a horizontal line, with angle $ 43^\circ $, and angles labeled 1, 2, 3

From the diagram:

- Angle 1 is vertical to $ 43^\circ $ → $ \angle 1 = 43^\circ $
- Angle 2 is adjacent to $ 43^\circ $, forming a straight line → supplementary
$$
\angle 2 = 180^\circ - 43^\circ = 137^\circ
$$
- Angle 3 is vertical to $ \angle 2 $, so $ \angle 3 = 137^\circ $

✔ Answers:
- $ \angle 1 = 43^\circ $
- $ \angle 2 = 137^\circ $
- $ \angle 3 = 137^\circ $

Reasoning:
- Vertical angles are equal.
- Adjacent angles on a straight line are supplementary (add to 180°).

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11.

Diagram: Two perpendicular lines and a diagonal line crossing them, forming angles $ a, b, c, d, e $

#### a) Vertical angles:
Vertical angles are opposite angles formed by intersecting lines.

- $ a $ and $ c $ are vertical
- $ b $ and $ d $ are vertical
- $ e $ and $ ? $ — actually, $ e $ is opposite to another angle? Wait — let’s label carefully.

Actually, from the diagram:
- $ a $ and $ c $ are opposite → vertical
- $ b $ and $ d $ are opposite → vertical
- $ e $ and $ ? $ — but wait, there’s only five angles shown.

Wait — likely:
- Angles around point: $ a, b, c, d, e $

But more likely, the diagram shows:
- One vertical line, one horizontal line, and a diagonal line through origin.
- So three lines intersecting at one point → multiple pairs of vertical angles.

But typically in such problems:
- $ a $ and $ c $ are vertical
- $ b $ and $ d $ are vertical
- $ e $ and another angle? Actually, $ e $ might be adjacent.

But standard labeling:

Assuming:
- $ a $ and $ c $ are vertical
- $ b $ and $ d $ are vertical
- $ e $ and $ ? $ — perhaps $ e $ is opposite to $ b $? No.

Wait — better to assume:
- $ a $ and $ c $ are vertical
- $ b $ and $ d $ are vertical
- But $ e $ is not paired?

Wait — maybe the diagram has:
- Horizontal and vertical lines (perpendicular), so 90° angles
- Diagonal line crosses both

So angles:
- $ a $: between horizontal and vertical → 90°
- $ b $: above diagonal
- $ c $: below diagonal
- $ d $: opposite $ b $
- $ e $: opposite $ c $

But from the diagram:
- $ a $ is a right angle (marked)
- $ b $ and $ c $ are adjacent to $ a $
- $ d $ and $ e $ are opposite

Actually, from standard interpretation:

Let’s assume:
- $ a $ and $ c $ are vertical → yes
- $ b $ and $ d $ are vertical → yes
- $ e $ and $ ? $ — maybe $ e $ is opposite to $ b $? Not clear.

But looking at common problems like this:

Typical setup:
- $ a $ and $ c $ are vertical
- $ b $ and $ d $ are vertical
- $ e $ and $ b $ are adjacent, etc.

But since $ a $ is marked as a right angle (square), then $ a = 90^\circ $

Now:

#### a) Vertical angles:
- $ a $ and $ c $ → vertical
- $ b $ and $ d $ → vertical
- $ e $ and $ ? $ — actually, $ e $ and $ b $ may not be vertical unless symmetric.

But likely:
- $ a $ and $ c $ are vertical
- $ b $ and $ d $ are vertical
- $ e $ and $ b $ are not vertical — unless mislabeled.

Wait — perhaps $ e $ is the same as $ d $? Or $ e $ is adjacent.

But from the diagram:
- $ a $ is top-left quadrant
- $ b $ is top-right
- $ c $ is bottom-right
- $ d $ is bottom-left
- $ e $ is between $ a $ and $ b $? No.

Wait — perhaps the labels are:
- $ a $: top-left (between vertical and horizontal)
- $ b $: top-right (between vertical and diagonal)
- $ c $: bottom-right (between diagonal and horizontal)
- $ d $: bottom-left (between horizontal and diagonal)
- $ e $: left side (between vertical and diagonal)

This is confusing.

But standard way:

In such diagrams:
- $ a $ and $ c $ are vertical angles
- $ b $ and $ d $ are vertical angles
- $ e $ and $ ? $ — maybe $ e $ is not vertical

But since $ a $ is 90°, and the lines are perpendicular, then:

Let’s re-analyze:

Assume:
- The horizontal and vertical lines are perpendicular → $ a = 90^\circ $
- Diagonal line crosses them

Then:
- $ a $ and $ c $ are vertical → $ c = 90^\circ $
- $ b $ and $ d $ are vertical → $ b = d $
- $ e $ and $ ? $ — probably $ e $ is adjacent to $ a $

But $ e $ is labeled near $ a $, so maybe $ e $ is the angle between vertical and diagonal.

Wait — perhaps the diagram shows:

- $ a $: between horizontal and vertical → 90°
- $ b $: between vertical and diagonal
- $ c $: between diagonal and horizontal
- $ d $: opposite $ b $
- $ e $: opposite $ c $

Then:
- $ b $ and $ d $ are vertical
- $ c $ and $ e $ are vertical
- $ a $ and $ ? $ — $ a $ is not vertical with anyone unless $ a $ is opposite $ c $? But $ c $ is not 90°

But $ a $ is 90°, and if the lines are perpendicular, then $ a = 90^\circ $, and $ c $ is not necessarily 90° unless diagonal is aligned.

Wait — no, $ a $ is marked with a square → 90°, so the horizontal and vertical lines are perpendicular.

So $ a = 90^\circ $

Now, the diagonal cuts through.

So:
- $ a $ is 90°
- $ b $: angle between vertical and diagonal
- $ c $: angle between diagonal and horizontal
- $ d $: opposite $ b $
- $ e $: opposite $ c $

Then:
- $ b $ and $ d $ are vertical → equal
- $ c $ and $ e $ are vertical → equal
- $ a $ and $ ? $ — $ a $ is not vertical with any single angle unless we consider the full angle

But $ a $ is 90°, and adjacent to $ b $ and $ e $? Not sure.

But likely:

#### a) Vertical angles:
- $ b $ and $ d $
- $ c $ and $ e $

But $ a $ is 90°, and no opposite angle labeled — but $ a $ is adjacent to $ b $ and $ e $? Probably not.

Wait — maybe $ a $ and $ c $ are vertical? Only if $ c $ is also 90°, which would require diagonal to be horizontal or vertical — not possible.

So likely:

✔ a) Vertical angles: $ b $ and $ d $, $ c $ and $ e $

But the question says "Name the angles" — so list pairs.

So:
- $ b $ and $ d $
- $ c $ and $ e $

But $ a $ is alone? Maybe $ a $ is not vertical with another labeled angle.

But wait — $ a $ is between horizontal and vertical → 90°, and $ c $ is between diagonal and horizontal — not necessarily 90°.

So vertical angles:
- $ b $ and $ d $
- $ c $ and $ e $

✔ a) Vertical: $ b $ and $ d $, $ c $ and $ e $

But sometimes $ a $ is considered — but not vertical with any labeled angle unless $ a $ and $ c $ are opposite — but they’re not.

Wait — maybe $ a $ and $ c $ are vertical? Only if the diagonal is at 45°, but not necessarily.

But given $ a $ is 90°, and $ c $ is not necessarily 90°, so not vertical.

So best answer:
- $ b $ and $ d $
- $ c $ and $ e $

✔ a) Vertical: $ b $ and $ d $, $ c $ and $ e $

#### b) Complementary: $ \angle c $ and ______

Complementary angles sum to 90°.

We know $ a = 90^\circ $. Since $ a $ is made of $ b $ and $ e $? Or $ a $ is adjacent to $ b $ and $ e $? Not clear.

Wait — $ a $ is the angle between horizontal and vertical — 90°.

The diagonal splits the plane.

So:
- $ a $: 90°
- $ b $: angle between vertical and diagonal
- $ e $: angle between vertical and diagonal (on other side)? No.

Wait — better to think:

At the intersection point:
- The horizontal and vertical lines make four 90° angles.
- The diagonal cuts through, creating new angles.

So:
- $ a $: one 90° angle
- $ b $: part of the angle between vertical and diagonal
- $ c $: part of angle between diagonal and horizontal
- $ d $: opposite $ b $
- $ e $: opposite $ c $

But $ a $ is already 90°, so $ b $ and $ e $ must be adjacent to $ a $.

Wait — maybe $ a $ is the angle between horizontal and vertical → 90°
Then $ b $ is the angle between vertical and diagonal (say, $ x $)
Then $ e $ is the angle between vertical and diagonal on the other side → $ x $
But that can’t be.

Wait — perhaps the diagram shows:

- $ a $: 90° (horizontal-vertical)
- $ b $: angle between vertical and diagonal
- $ c $: angle between diagonal and horizontal
- $ d $: opposite $ b $
- $ e $: opposite $ c $

Then $ b + c = 90^\circ $? Because $ a $ is 90°, and $ b $ and $ c $ are adjacent to it?

No — $ b $ and $ c $ are not adjacent to $ a $ — they are in different quadrants.

Actually, $ a $ is in one quadrant, $ b $ in another, etc.

But since $ a = 90^\circ $, and $ b $ is in the same region? No.

Wait — perhaps $ a $ is the angle between horizontal and vertical → 90°
Then $ b $ is the angle between vertical and diagonal — say $ x $
Then $ c $ is the angle between diagonal and horizontal — say $ y $
Then $ x + y = 90^\circ $ — because they are adjacent to $ a $?

No — $ a $ is 90°, but $ b $ and $ c $ are in adjacent quadrants.

Actually, the total angle around a point is 360°.

But if $ a = 90^\circ $, and the lines are perpendicular, then the four angles from horizontal/vertical are all 90°.

But the diagonal cuts through, so it splits some angles.

So for example:
- In the top-right quadrant: angle $ b $ is part of the 90° angle
- But $ b $ is between vertical and diagonal
- $ c $ is between diagonal and horizontal
- So $ b + c = 90^\circ $ — because they make up the 90° angle of the quadrant

Yes!

So in the top-right quadrant:
- $ b $ and $ c $ are adjacent and together make the 90° angle
- So $ b + c = 90^\circ $ → complementary

Similarly, in other quadrants.

So:
- $ \angle c $ and $ \angle b $ are complementary

✔ b) Complementary: $ \angle c $ and $ \angle b $

#### c) Supplementary: $ \angle c $ and ______

Supplementary angles sum to 180°.

$ \angle c $ and its adjacent angle on the straight line.

For example, $ \angle c $ and $ \angle d $ — are they adjacent? If $ d $ is opposite $ b $, then $ c $ and $ d $ may not be adjacent.

Wait — $ \angle c $ is in the bottom-right quadrant, $ \angle d $ is in the bottom-left — not adjacent.

But $ \angle c $ and $ \angle e $ — $ e $ is opposite $ c $ → vertical → equal, not supplementary.

Supplementary means they add to 180°.

So $ \angle c $ and the angle next to it on the same line.

For example, $ \angle c $ and $ \angle b $ — no, they are complementary.

Wait — $ \angle c $ and $ \angle d $ — not adjacent.

Wait — look at the horizontal line: $ \angle c $ is on one side, $ \angle e $ is on the other side? No.

Wait — perhaps $ \angle c $ and $ \angle e $ are adjacent along the horizontal line?

If $ c $ is between diagonal and horizontal, and $ e $ is between diagonal and horizontal on the other side, then $ c $ and $ e $ are adjacent?

No — they are on opposite sides.

Actually, $ \angle c $ and $ \angle e $ are vertical — so equal.

But supplementary would be $ \angle c $ and the angle next to it on the straight line.

For example, if $ \angle c $ is in the bottom-right, then the angle adjacent to it along the horizontal line is $ \angle d $? No.

Wait — perhaps $ \angle c $ and $ \angle b $ are adjacent? No.

Better: $ \angle c $ and $ \angle a $ — not adjacent.

Wait — the horizontal line: angles on one side are $ \angle c $ and $ \angle d $? No.

Perhaps the horizontal line has:
- On the right: $ \angle c $
- On the left: $ \angle e $ — but $ e $ is not on horizontal.

Wait — this is getting messy.

Alternative approach:

Since $ \angle c $ and $ \angle e $ are vertical → equal

But $ \angle c $ and $ \angle b $ are complementary → sum to 90°

But $ \angle c $ and $ \angle d $ — $ d $ is vertical to $ b $, so $ d = b $

Then $ c + d = c + b = 90^\circ $ — still not 180°

Wait — what about $ \angle c $ and $ \angle a $? $ a = 90^\circ $, $ c $ is less than 90° — sum < 180°

Not helpful.

Wait — perhaps $ \angle c $ and $ \angle d $ are not adjacent.

But $ \angle c $ and $ \angle b $ are in the same quadrant — but not on a straight line.

Wait — the diagonal line: $ \angle c $ and $ \angle b $ are on opposite sides of the diagonal? No.

Actually, $ \angle c $ and $ \angle d $ are not adjacent.

But $ \angle c $ and $ \angle e $ are vertical → not supplementary.

Wait — the only way for $ \angle c $ to be supplementary is with the angle adjacent to it on a straight line.

For example, if $ \angle c $ is between diagonal and horizontal, then the angle adjacent to it along the horizontal line is $ \angle d $? No.

Wait — perhaps $ \angle c $ and $ \angle e $ are adjacent along the diagonal? No.

Wait — let’s think differently.

Suppose the horizontal line is straight. Then angles on one side must add to 180°.

So $ \angle c $ and $ \angle d $ — are they on the same straight line?

If $ \angle c $ is in the bottom-right, and $ \angle d $ is in the bottom-left, then they are on the same horizontal line — yes!

So $ \angle c $ and $ \angle d $ are adjacent and on a straight line → supplementary

So:
$$
\angle c + \angle d = 180^\circ
$$

Similarly, $ \angle b $ and $ \angle e $ are on the vertical line — supplementary.

So:
- $ \angle c $ and $ \angle d $ are supplementary

✔ c) Supplementary: $ \angle c $ and $ \angle d $

#### d) All adjacent angles:

Adjacent angles share a common side and vertex.

So:
- $ a $ and $ b $: adjacent (share vertical line)
- $ a $ and $ e $: adjacent (share vertical line)
- $ b $ and $ c $: adjacent (share diagonal)
- $ c $ and $ d $: adjacent (share horizontal)
- $ d $ and $ e $: adjacent (share diagonal)
- $ e $ and $ a $: adjacent (share vertical)

Also:
- $ b $ and $ d $: not adjacent — opposite
- $ c $ and $ e $: not adjacent — opposite

So adjacent pairs:
- $ a $ and $ b $
- $ a $ and $ e $
- $ b $ and $ c $
- $ c $ and $ d $
- $ d $ and $ e $
- $ e $ and $ a $

But the question asks to “name the angles” — probably list all adjacent pairs.

But likely, just list them.

✔ d) All adjacent: $ a $ and $ b $, $ a $ and $ e $, $ b $ and $ c $, $ c $ and $ d $, $ d $ and $ e $, $ e $ and $ a $

But perhaps simplified.

#### e) Find values of all angles, if $ \angle c = 30^\circ $

Given $ \angle c = 30^\circ $

From earlier:
- $ \angle c $ and $ \angle b $ are complementary → $ b + c = 90^\circ $
$$
b = 90^\circ - 30^\circ = 60^\circ
$$
- $ \angle b $ and $ \angle d $ are vertical → $ d = b = 60^\circ $
- $ \angle c $ and $ \angle e $ are vertical → $ e = c = 30^\circ $
- $ \angle a = 90^\circ $ (given, right angle)

So:
- $ a = 90^\circ $
- $ b = 60^\circ $
- $ c = 30^\circ $
- $ d = 60^\circ $
- $ e = 30^\circ $

✔ e) Values:
- $ a = 90^\circ $
- $ b = 60^\circ $
- $ c = 30^\circ $
- $ d = 60^\circ $
- $ e = 30^\circ $

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✔ Final Answers:

#### 1. Supplementary, $ x = 60^\circ $
#### 2. Vertical, $ x = 119^\circ $
#### 3. Complementary, $ x = 35^\circ $
#### 4. Supplementary, $ x = 140^\circ $
#### 5. Complementary, $ x = 10^\circ $
#### 6. Supplementary, $ x = 82^\circ $
#### 7. Complementary, $ x = 68^\circ $
#### 8. Vertical, $ x = 59^\circ $
#### 9. Supplementary, $ x = 174^\circ $
#### 10.
- $ \angle 1 = 43^\circ $
- $ \angle 2 = 137^\circ $
- $ \angle 3 = 137^\circ $
- Reasoning: $ \angle 1 $ is vertical to $ 43^\circ $, $ \angle 2 $ is supplementary to $ 43^\circ $, $ \angle 3 $ is vertical to $ \angle 2 $

#### 11.
a) Vertical: $ b $ and $ d $, $ c $ and $ e $
b) Complementary: $ \angle c $ and $ \angle b $
c) Supplementary: $ \angle c $ and $ \angle d $
d) All adjacent: $ a $ and $ b $, $ a $ and $ e $, $ b $ and $ c $, $ c $ and $ d $, $ d $ and $ e $, $ e $ and $ a $
e) $ a = 90^\circ $, $ b = 60^\circ $, $ c = 30^\circ $, $ d = 60^\circ $, $ e = 30^\circ $

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