Linear Pairs of Angles Worksheets - Free Printable

Let's solve each part of the Linear Pairs worksheet step by step.

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Part A: Find the measure of the indicated angle in each linear pair.

A linear pair consists of two adjacent angles that form a straight line. Their measures add up to 180°.

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#### 1)
We are given an angle of 58°, and we need to find $ m\angle 1 $, which is its supplement.

$$
m\angle 1 = 180^\circ - 58^\circ = 122^\circ
$$

✔ Answer: $ \boxed{122^\circ} $

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#### 2)
Given: $ m\angle 2 = 127^\circ $

$$
m\angle DGH = 180^\circ - 127^\circ = 53^\circ
$$

✔ Answer: $ \boxed{53^\circ} $

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#### 3)
Given: $ m\angle 3 = 149^\circ $

$$
m\angle GCP = 180^\circ - 149^\circ = 31^\circ
$$

✔ Answer: $ \boxed{31^\circ} $

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#### 4)
Given: $ m\angle 4 = 62^\circ $

$$
m\angle BDE = 180^\circ - 62^\circ = 118^\circ
$$

✔ Answer: $ \boxed{118^\circ} $

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Part B: If ∠1 and ∠2 form a linear pair and $ m\angle 1 = 2 \times m\angle 2 $, find the measures of the angles.

Let:
- $ m\angle 2 = x $
- Then $ m\angle 1 = 2x $

Since they form a linear pair:

$$
m\angle 1 + m\angle 2 = 180^\circ \\
2x + x = 180^\circ \\
3x = 180^\circ \\
x = 60^\circ
$$

So:
- $ m\angle 2 = 60^\circ $
- $ m\angle 1 = 2 \times 60^\circ = 120^\circ $

✔ Answer: $ \boxed{120^\circ} $ and $ \boxed{60^\circ} $

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C: If the difference in the measures of a linear pair of angles is $ 42^\circ $, find the measures of the angles.

Let the two angles be $ x $ and $ y $. Since they are a linear pair:

$$
x + y = 180^\circ \quad \text{(1)}
$$

And the difference is $ 42^\circ $. Assume $ x > y $, so:

$$
x - y = 42^\circ \quad \text{(2)}
$$

Now solve the system:

Add equations (1) and (2):

$$
(x + y) + (x - y) = 180 + 42 \\
2x = 222 \\
x = 111^\circ
$$

Substitute into (1):

$$
111 + y = 180 \Rightarrow y = 69^\circ
$$

✔ Answer: $ \boxed{111^\circ} $ and $ \boxed{69^\circ} $

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D: Two angles form a linear pair. If the measure of one angle is five times the measure of the other, what are the measures of the angles?

Let:
- Smaller angle = $ x $
- Larger angle = $ 5x $

They form a linear pair:

$$
x + 5x = 180^\circ \\
6x = 180^\circ \\
x = 30^\circ
$$

So:
- Smaller angle = $ 30^\circ $
- Larger angle = $ 5 \times 30^\circ = 150^\circ $

✔ Answer: $ \boxed{30^\circ} $ and $ \boxed{150^\circ} $

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✔ Final Answers Summary:

A)
1) $ 122^\circ $
2) $ 53^\circ $
3) $ 31^\circ $
4) $ 118^\circ $

B) $ 120^\circ $ and $ 60^\circ $

C) $ 111^\circ $ and $ 69^\circ $

D) $ 30^\circ $ and $ 150^\circ $

Let me know if you'd like this as a printable solution or with diagrams!