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:
> If two angles form a linear pair:
> $$
> \text{Angle 1} + \text{Angle 2} = 180^\circ
> $$
So, to find the missing angle:
$$
\text{Missing angle} = 180^\circ - \text{Given angle}
$$
---
1)
- Given: $ m\angle DOF = ? $
- One angle is $ 34^\circ $
- These two angles form a linear pair.
$$
m\angle DOF = 180^\circ - 34^\circ = 146^\circ
$$
✔ Answer: 146°
---
2)
- Given: $ m\angle GOH = ? $
- One angle is $ 105^\circ $
$$
m\angle GOH = 180^\circ - 105^\circ = 75^\circ
$$
✔ Answer: 75°
---
3)
- Given: $ m\angle BOC = ? $
- One angle is $ 135^\circ $
$$
m\angle BOC = 180^\circ - 135^\circ = 45^\circ
$$
✔ Answer: 45°
---
4)
- Given: $ m\angle LON = ? $
- One angle is $ 69^\circ $
$$
m\angle LON = 180^\circ - 69^\circ = 111^\circ
$$
✔ Answer: 111°
---
5)
- Given: $ m\angle SOU = ? $
- One angle is $ 17^\circ $
$$
m\angle SOU = 180^\circ - 17^\circ = 163^\circ
$$
✔ Answer: 163°
---
6)
- Given: $ m\angle VOZ = ? $
- One angle is $ 114^\circ $
$$
m\angle VOZ = 180^\circ - 114^\circ = 66^\circ
$$
✔ Answer: 66°
---
7)
- Given: $ m\angle ROS = ? $
- One angle is $ 38^\circ $
$$
m\angle ROS = 180^\circ - 38^\circ = 142^\circ
$$
✔ Answer: 142°
---
8)
- Given: $ m\angle UOW = ? $
- One angle is $ 58^\circ $
$$
m\angle UOW = 180^\circ - 58^\circ = 122^\circ
$$
✔ Answer: 122°
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1) | 146° |
| 2) | 75° |
| 3) | 45° |
| 4) | 111° |
| 5) | 163° |
| 6) | 66° |
| 7) | 142° |
| 8) | 122° |
---
🔍 Explanation Summary:
Each pair of angles forms a
straight line, so they are
supplementary (add to 180°). We subtract the given angle from 180° to get the unknown angle.
Let me know if you'd like this formatted for printing or as a worksheet!
Parent Tip: Review the logic above to help your child master the concept of linear pair worksheet.
