Let’s solve each problem step by step using the
Triangle Angle Sum Theorem (interior angles of a triangle add up to 180°) and the
Exterior Angle Theorem (an exterior angle equals the sum of the two remote interior angles).
---
Problem 1: ∠ECD = ?
We are given:
- ∠D = 21°
- ∠E = 31°
∠ECD is an
exterior angle at vertex C, formed by extending side DC to point E.
✔ Exterior Angle Theorem:
> Exterior angle = sum of two non-adjacent interior angles.
So,
> ∠ECD = ∠D + ∠E = 21° + 31° =
52°
✔️
Answer: 52°
---
Problem 2: ∠TQR = ?
Triangle TQR:
- ∠T = 55°
- ∠R = 39°
Find ∠Q (which is ∠TQR).
✔ Triangle Angle Sum Theorem:
> ∠T + ∠Q + ∠R = 180°
> 55° + ∠Q + 39° = 180°
> ∠Q = 180° - 55° - 39° =
86°
✔️
Answer: 86°
---
Problem 3: ∠MNP = ?
This is an
exterior angle at vertex N, formed by extending side PN to M.
Given:
- ∠O = 77°
- ∠P = 77°
✔ Exterior Angle Theorem:
> ∠MNP = ∠O + ∠P = 77° + 77° =
154°
✔️
Answer: 154°
---
Problem 4: ∠MOQ = ?
This is an
exterior angle at vertex O, formed by extending side QO to M.
Given:
- ∠P = 87°
- ∠Q = 63°
✔ Exterior Angle Theorem:
> ∠MOQ = ∠P + ∠Q = 87° + 63° =
150°
✔️
Answer: 150°
---
Problem 5: ∠NPM = ?
Triangle MNP:
- ∠M = 60°
- ∠N = 60°
Find ∠P (∠NPM).
✔ Triangle Angle Sum Theorem:
> ∠M + ∠N + ∠P = 180°
> 60° + 60° + ∠P = 180°
> ∠P = 180° - 120° =
60°
✔️
Answer: 60°
*(Note: This is an equilateral triangle!)*
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Problem 6: ∠HFX = ?
This is an
exterior angle at vertex F, formed by extending side HF to X.
Given:
- ∠H = 39°
- ∠W = 26°
✔ Exterior Angle Theorem:
> ∠HFX = ∠H + ∠W = 39° + 26° =
65°
✔️
Answer: 65°
---
Problem 7: ∠RPQ = ?
Triangle PQR:
- ∠Q = 51°
- ∠R = 46°
Find ∠P (∠RPQ).
✔ Triangle Angle Sum Theorem:
> ∠P + 51° + 46° = 180°
> ∠P = 180° - 97° =
83°
✔️
Answer: 83°
---
Problem 8: ∠XAC = ?
This is an
exterior angle at vertex A, formed by extending side BA to X.
Given:
- ∠B = 47°
- ∠C = 60°
✔ Exterior Angle Theorem:
> ∠XAC = ∠B + ∠C = 47° + 60° =
107°
✔️
Answer: 107°
---
##
✔ Final Answers:
1.
∠ECD = 52°
2.
∠TQR = 86°
3.
∠MNP = 154°
4.
∠MOQ = 150°
5.
∠NPM = 60°
6.
∠HFX = 65°
7.
∠RPQ = 83°
8.
∠XAC = 107°
Let me know if you’d like a diagram or visual explanation for any of these!
Parent Tip: Review the logic above to help your child master the concept of exterior angles of triangles worksheet.
