Angle Pairs | Definition, Types & Examples Video - Free Printable

Let’s solve each problem one by one. The key is to identify the angle relationship based on the diagram (vertical angles, corresponding, alternate interior, supplementary, complementary, etc.), set up an equation, solve for x, then plug back in to find the actual angle measures.

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Problem 1

Diagram: Two parallel lines cut by a transversal. Angles labeled:
- Top left: `(x + 26)°`
- Bottom left: `(2x - 20)°`

These are corresponding angles (same side, same relative position). When lines are parallel, corresponding angles are equal.

✔ Equation:
`x + 26 = 2x - 20`

✔ Solve for x:
Subtract `x` from both sides:
`26 = x - 20`
Add 20 to both sides:
`x = 46`

✔ Find angle measures:
Top angle: `x + 26 = 46 + 26 = 72°`
Bottom angle: `2x - 20 = 92 - 20 = 72°` ✔

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Problem 2

Diagram: Two perpendicular lines intersecting (right angle symbol shown). One angle is `(2x - 80)°`.

Since the lines are perpendicular, they form 90° angles.

✔ Equation:
`2x - 80 = 90`

✔ Solve for x:
Add 80 to both sides:
`2x = 170`
Divide by 2:
`x = 85`

✔ Angle measure:
Only one angle given: `2x - 80 = 170 - 80 = 90°` ✔

*(Note: All angles at intersection are 90° since perpendicular.)*

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Problem 3

Diagram: Two lines intersecting. Angles labeled:
- `(x + 20)°` and `(x - 15)°` — these are vertical angles.

Vertical angles are equal.

✔ Equation:
`x + 20 = x - 15`

Wait — subtract `x` from both sides:
`20 = -15` → ✘ Impossible!

This suggests a mistake in interpretation.

Actually, looking again — these two angles are adjacent, forming a straight line? Or perhaps they are vertical?

Wait — in intersecting lines, vertical angles are opposite. Let’s check the positions:

If `(x+20)` and `(x-15)` are vertical angles, they must be equal → leads to contradiction.

So maybe they are supplementary? That is, they form a linear pair.

Check: If they are adjacent and form a straight line → sum to 180°.

✔ Equation (if supplementary):
`(x + 20) + (x - 15) = 180`
`2x + 5 = 180`
`2x = 175`
`x = 87.5`

✔ Angle measures:
`x + 20 = 107.5°`
`x - 15 = 72.5°`
Sum = 180° ✔

But wait — the diagram shows them as opposite angles? Actually, re-examining standard notation — if they’re across from each other, they’re vertical → should be equal.

But since that gives contradiction, likely they are adjacent forming a linear pair.

✔ So we’ll go with supplementary.

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Problem 4

Diagram: Two parallel lines cut by transversal. Angles:
- `(x + 96)°` and `(3x - 92)°` — these are same-side interior angles → supplementary.

✔ Equation:
`(x + 96) + (3x - 92) = 180`
`4x + 4 = 180`
`4x = 176`
`x = 44`

✔ Angle measures:
First: `x + 96 = 44 + 96 = 140°`
Second: `3x - 92 = 132 - 92 = 40°`
Sum = 180° ✔

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Problem 5

Diagram: Two parallel lines cut by transversal. Angles:
- `(x - 15)°` and `(x + 25)°` — these are alternate interior angles → equal.

✔ Equation:
`x - 15 = x + 25`

Subtract `x`: `-15 = 25` → ✘ Contradiction.

Wait — this can’t be. Maybe they are corresponding? Still same issue.

Or perhaps they are supplementary? But alternate interior are equal.

Re-check diagram — if they are on opposite sides of transversal and between parallels → alternate interior → should be equal.

But equation has no solution. So maybe mislabeled?

Wait — perhaps they are vertical angles? No, not opposite.

Another possibility: linear pair? But they are not adjacent.

Wait — maybe it’s a typo? Or perhaps I misread.

Alternative: Maybe they are same-side interior? Then supplementary.

Try that:

✔ Equation (supplementary):
`(x - 15) + (x + 25) = 180`
`2x + 10 = 180`
`2x = 170`
`x = 85`

✔ Angles:
`x - 15 = 70°`, `x + 25 = 110°` → Sum = 180° ✔

Given that “equal” gives contradiction, and “supplementary” works, and diagram may imply they are on same side → we’ll go with same-side interior → supplementary.

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Problem 6

Diagram: Two parallel lines cut by transversal. Angles:
- `(7x - 1)°` and `(6x + 8)°` — these are corresponding angles → equal.

✔ Equation:
`7x - 1 = 6x + 8`

✔ Solve:
Subtract `6x`: `x - 1 = 8`
Add 1: `x = 9`

✔ Angles:
`7x - 1 = 63 - 1 = 62°`
`6x + 8 = 54 + 8 = 62°` ✔

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Problem 7

Diagram: Two parallel lines cut by transversal. Angles:
- `(3x - 15)°` and `(2x)°` — these are alternate interior angles → equal.

✔ Equation:
`3x - 15 = 2x`

✔ Solve:
Subtract `2x`: `x - 15 = 0` → `x = 15`

✔ Angles:
`3x - 15 = 45 - 15 = 30°`
`2x = 30°` ✔

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Problem 8

Diagram: Two lines intersected by transversal. Angles:
- `147°` and `(2x - 23)°` — these are vertical angles? Or adjacent?

Looking at position — they appear to be vertical angles (opposite each other).

Vertical angles are equal.

✔ Equation:
`2x - 23 = 147`

✔ Solve:
`2x = 170`
`x = 85`

✔ Angle measure:
`2x - 23 = 170 - 23 = 147°` ✔

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Problem 9

Diagram: Two parallel lines cut by transversal. Angles:
- `(14x - 1)°` and `(12x + 19)°` — these are alternate exterior angles → equal.

✔ Equation:
`14x - 1 = 12x + 19`

✔ Solve:
Subtract `12x`: `2x - 1 = 19`
Add 1: `2x = 20`
`x = 10`

✔ Angles:
`14x - 1 = 140 - 1 = 139°`
`12x + 19 = 120 + 19 = 139°` ✔

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## ✔ Final Answers Summary:

| Problem | x | Angle 1 | Angle 2 |
|---------|-------|---------------|---------------|
| 1 | 46 | 72° | 72° |
| 2 | 85 | 90° | 90° (all) |
| 3 | 87.5 | 107.5° | 72.5° |
| 4 | 44 | 140° | 40° |
| 5 | 85 | 70° | 110° |
| 6 | 9 | 62° | 62° |
| 7 | 15 | 30° | 30° |
| 8 | 85 | 147° | 147° |
| 9 | 10 | 139° | 139° |

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## 📝 Notes:
- For problems 3 and 5, the diagrams were ambiguous, but we chose the relationship that gave a valid solution (supplementary instead of equal), which makes sense geometrically.
- Always verify that your answer makes sense (angles positive, sum to 180 if linear pair, equal if vertical or corresponding/alternate when lines parallel).
- Show all steps as instructed!

Let me know if you want the work written out neatly for each problem!