Pairs of Angles Worksheets - Free Printable

Let's solve each problem step by step from the worksheet titled "Pairs of Angles - Find x". We'll use angle relationships such as:

- Supplementary angles: Two angles that add up to 180° (form a straight line).
- Complementary angles: Two angles that add up to 90°.
- Vertical angles: Opposite angles formed by intersecting lines; they are equal.
- Adjacent angles: Share a common vertex and side, but do not overlap.

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Problem 11

Given:
- One angle is $40^\circ$
- The other angle is labeled $x$

These two angles form a straight line → supplementary

$$
x + 40^\circ = 180^\circ \\
x = 180^\circ - 40^\circ = 140^\circ
$$

✔ Answer: $x = 140^\circ$

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Problem 22

Given:
- One angle is $31^\circ$
- The other angle is $x$, and they form a straight line

So:
$$
x + 31^\circ = 180^\circ \\
x = 180^\circ - 31^\circ = 149^\circ
$$

✔ Answer: $x = 149^\circ$

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Problem 33

Given:
- One angle is $50^\circ$
- Another angle is $x$, and both are adjacent on a straight line

Wait — actually, the diagram shows two angles forming a straight line with one marked $50^\circ$ and the other $x$. But there’s a small angle between them?

Wait — let's re-analyze.

Actually, in Problem 33:
- A ray splits a straight line into two angles: $x$ and $50^\circ$, and they're adjacent and form a straight line.

So:
$$
x + 50^\circ = 180^\circ \\
x = 130^\circ
$$

✔ Answer: $x = 130^\circ$

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Problem 44

Given:
- An angle is $110^\circ$, and it forms a straight line with $x$

So:
$$
x + 110^\circ = 180^\circ \\
x = 70^\circ
$$

✔ Answer: $x = 70^\circ$

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Problem 55

Given:
- Two angles: $x$ and $70^\circ$, and they appear to be vertical angles or part of a triangle?

Looking closely: The diagram shows two intersecting lines forming an "X". One angle is $70^\circ$, and opposite to it is $x$. So they are vertical angles.

Vertical angles are equal.

So:
$$
x = 70^\circ
$$

✔ Answer: $x = 70^\circ$

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Problem 66

Given:
- Two angles: $120^\circ$ and $x$, and they are adjacent on a straight line

So:
$$
x + 120^\circ = 180^\circ \\
x = 60^\circ
$$

✔ Answer: $x = 60^\circ$

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Problem 77

Given:
- A triangle-like figure with angles $x$, $40^\circ$, and $70^\circ$

Wait — this looks like a triangle? Or three angles around a point?

But the diagram shows three rays from a single point, forming three angles: $x$, $40^\circ$, and $70^\circ$, and they all meet at a point forming a full circle?

No — actually, looking at the diagram, it appears that $x$, $40^\circ$, and $70^\circ$ are adjacent angles forming a straight line?

Wait — no, they seem to be angles around a point?

But more likely: the diagram shows a straight line with a point where three rays come out, but only two angles are labeled: $x$, $40^\circ$, and $70^\circ$.

Wait — actually, the diagram shows a straight line with a ray going upward. The angles are:
- Between the horizontal line and the ray: $x$
- Then $40^\circ$ and $70^\circ$ are shown above the ray?

Wait — better interpretation:

It seems like a straight line with a transversal. But the label says: $x$, then $40^\circ$, then $70^\circ$, and they are adjacent angles along a straight line.

So total: $x + 40^\circ + 70^\circ = 180^\circ$

$$
x + 110^\circ = 180^\circ \\
x = 70^\circ
$$

✔ Answer: $x = 70^\circ$

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Problem 88

Given:
- Two angles: $60^\circ$ and $x$, and they are vertical angles

They are opposite angles formed by two intersecting lines.

So vertical angles are equal → $x = 60^\circ$

✔ Answer: $x = 60^\circ$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 11 | $x = 140^\circ$ |
| 22 | $x = 149^\circ$ |
| 33 | $x = 130^\circ$ |
| 44 | $x = 70^\circ$ |
| 55 | $x = 70^\circ$ |
| 66 | $x = 60^\circ$ |
| 77 | $x = 70^\circ$ |
| 88 | $x = 60^\circ$ |

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🔍 Summary of Concepts Used:

- Straight line = 180° → supplementary angles
- Vertical angles are equal
- Angles around a point = 360°, but here mostly linear pairs

Let me know if you'd like a visual explanation or want to print these answers!