Let's solve each problem step by step. The task is to
find the measure of the indicated angle in each linear pair.
A
linear pair consists of two adjacent angles that form a straight line, meaning their measures add up to
180°.
We’ll use the formula:
> $$
> \text{m} \angle A + \text{m} \angle B = 180^\circ
> $$
So:
> $$
> \text{m} \angle B = 180^\circ - \text{m} \angle A
> $$
---
1)
Given:
- One angle is $ 34^\circ $
- We need to find $ m\angle DOF $
Since they form a linear pair:
$$
m\angle DOF = 180^\circ - 34^\circ = 146^\circ
$$
✔ Answer: 146°
---
2)
Given:
- One angle is $ 105^\circ $
- Find $ m\angle GOH $
Linear pair:
$$
m\angle GOH = 180^\circ - 105^\circ = 75^\circ
$$
✔ Answer: 75°
---
3)
Given:
- One angle is $ 135^\circ $
- Find $ m\angle BOC $
$$
m\angle BOC = 180^\circ - 135^\circ = 45^\circ
$$
✔ Answer: 45°
---
4)
Given:
- One angle is $ 99^\circ $
- Find $ m\angle SON $
$$
m\angle SON = 180^\circ - 99^\circ = 81^\circ
$$
✔ Answer: 81°
---
5)
Given:
- One angle is $ 117^\circ $
- Find $ m\angle SOU $
$$
m\angle SOU = 180^\circ - 117^\circ = 63^\circ
$$
✔ Answer: 63°
---
6)
Given:
- One angle is $ 112^\circ $
- Find $ m\angle XOZ $
$$
m\angle XOZ = 180^\circ - 112^\circ = 68^\circ
$$
✔ Answer: 68°
---
7)
Given:
- One angle is $ 38^\circ $
- Find $ m\angle ROS $
$$
m\angle ROS = 180^\circ - 38^\circ = 142^\circ
$$
✔ Answer: 142°
---
8)
Given:
- One angle is $ 51^\circ $
- Find $ m\angle UOW $
$$
m\angle UOW = 180^\circ - 51^\circ = 129^\circ
$$
✔ Answer: 129°
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | 146° |
| 2 | 75° |
| 3 | 45° |
| 4 | 81° |
| 5 | 63° |
| 6 | 68° |
| 7 | 142° |
| 8 | 129° |
---
🔍 Explanation Summary:
- All problems involve
linear pairs, so the two angles are supplementary (sum to 180°).
- To find the missing angle, subtract the given angle from 180°.
- This applies regardless of the labeling or direction of the rays — as long as the two angles form a straight line.
Let me know if you'd like this formatted for printing or with diagrams!
Parent Tip: Review the logic above to help your child master the concept of angle pairs worksheet.
