Let's solve each of these
angle bisector problems step by step. The key concept here is:
> An
angle bisector divides an angle into
two equal parts.
So, if a ray (or segment) is an angle bisector, then the two angles it creates are
equal.
---
1) Find $ m\angle 2 $ if $ m\angle 1 = 20^\circ $.
- In triangle $ XYZ $, segment $ PZ $ is the angle bisector of $ \angle XZY $.
- $ \angle 1 $ and $ \angle 2 $ are the two parts created by the bisector.
- Since it's a bisector:
$$
m\angle 1 = m\angle 2
$$
- Given $ m\angle 1 = 20^\circ $, so:
$$
m\angle 2 = 20^\circ
$$
✔ Answer: C) 20°
---
2) Find $ m\angle 2 $ if $ m\angle 1 = 21^\circ $.
- Triangle $ YWX $, with $ PW $ as the angle bisector of $ \angle YWX $.
- So $ \angle 1 $ and $ \angle 2 $ are equal because of the bisector.
- Given $ m\angle 1 = 21^\circ $, so:
$$
m\angle 2 = 21^\circ
$$
✔ Answer: C) 21°
---
3) Find $ m\angle DFE $ if $ m\angle 2 = 18^\circ $.
- Triangle $ DEF $, with point $ P $ on $ DE $, and $ PF $ drawn to $ F $.
- $ \angle 2 $ is part of $ \angle DFE $, and since $ PF $ is the
angle bisector, it splits $ \angle DFE $ into two equal parts: $ \angle 1 $ and $ \angle 2 $.
- So $ m\angle 1 = m\angle 2 = 18^\circ $
- Therefore,
$$
m\angle DFE = \angle 1 + \angle 2 = 18^\circ + 18^\circ = 36^\circ
$$
✔ Answer: C) 36°
---
4) Find $ m\angle 1 $ if $ m\angle HFG = 58^\circ $.
- Triangle $ HFG $, with $ FP $ as the angle bisector of $ \angle HFG $.
- So $ \angle 1 $ and $ \angle 2 $ are equal halves of $ \angle HFG $.
- $ m\angle HFG = 58^\circ $, so:
$$
m\angle 1 = \frac{58^\circ}{2} = 29^\circ
$$
✔ Answer: B) 29°
---
5) $ m\angle TVU = 80^\circ $. Find $ m\angle 2 $.
- Triangle $ TUV $, with $ PV $ as the angle bisector of $ \angle TVU $.
- So $ \angle 1 $ and $ \angle 2 $ are equal parts of $ \angle TVU $.
- $ m\angle TVU = 80^\circ $, so:
$$
m\angle 2 = \frac{80^\circ}{2} = 40^\circ
$$
✔ Answer: D) 40°
---
6) Find $ m\angle 2 $ if $ m\angle 1 = 34^\circ $.
- Triangle $ XYZ $, with $ XP $ as the angle bisector of $ \angle ZXY $.
- $ \angle 1 $ and $ \angle 2 $ are the two equal parts.
- Given $ m\angle 1 = 34^\circ $, so:
$$
m\angle 2 = 34^\circ
$$
✔ Answer: C) 34°
---
7) $ m\angle YWX = 48^\circ $. Find $ m\angle 2 $.
- Triangle $ WYX $, with $ WP $ as the angle bisector of $ \angle YWX $.
- So $ \angle 1 $ and $ \angle 2 $ are equal.
- $ m\angle YWX = 48^\circ $, so:
$$
m\angle 2 = \frac{48^\circ}{2} = 24^\circ
$$
✔ Answer: B) 24°
---
✔ Final Answers Summary:
| Question | Answer |
|--------|--------|
| 1 | C) 20° |
| 2 | C) 21° |
| 3 | C) 36° |
| 4 | B) 29° |
| 5 | D) 40° |
| 6 | C) 34° |
| 7 | B) 24° |
---
🔍 Key Concept Recap:
>
An angle bisector divides an angle into two equal parts.
> So if you're given one of the smaller angles, the other is the same.
> If you're given the full angle, divide by 2 to get each half.
Let me know if you'd like a diagram explanation or more practice!
Parent Tip: Review the logic above to help your child master the concept of triangle angle bisector theorem worksheet.
