Worksheet for calculating missing interior angles in triangles, with nine problems showing two angles and asking to find the third.

I'll solve each triangle problem step by step, finding the missing angles using the fact that all angles in a triangle add up to 180°.

Problem 1: Triangle TUV with ∠T = 37° and ∠V = 63°
- Missing angle: ∠U
- Calculation: 180° - 37° - 63° = 80°
- m∠U = 80°

Problem 2: Right triangle ABC with ∠C = 90° (right angle) and ∠A = 46°
- Missing angle: ∠B
- Calculation: 180° - 90° - 46° = 44°
- m∠B = 44°

Problem 3: Triangle PQR with ∠P = 51° and ∠R = 36°
- Missing angle: ∠Q
- Calculation: 180° - 51° - 36° = 93°
- m∠Q = 93°

Problem 4: Triangle EFG with ∠G = 86° and ∠E = 47°
- Missing angle: ∠F
- Calculation: 180° - 86° - 47° = 47°
- m∠F = 47°

Problem 5: Triangle XYZ with ∠Z = 118° and ∠X = 33°
- Missing angle: ∠Y
- Calculation: 180° - 118° - 33° = 29°
- mY = 29°

Problem 6: Triangle UVW with ∠W = 42° and ∠U = 64°
- Missing angle: ∠V
- Calculation: 180° - 42° - 64° = 74°
- m∠V = 74°

Problem 7: Triangle KLM with ∠L = 60° and ∠M = 60°
- Missing angle: ∠K
- Calculation: 180° - 60° - 60° = 60°
- m∠K = 60°

Problem 8: Triangle STU with ∠S = 35° and ∠T = 35°
- Missing angle: ∠U
- Calculation: 180° - 35° - 35° = 110°
- m∠U = 110°

Problem 9: Triangle CDE with ∠E = 53° and ∠D = 77°
- Missing angle: ∠C
- Calculation: 180° - 53° - 77° = 50°
- m∠C = 50°

Let me verify my calculations:
1. 37 + 63 + 80 = 180 ✓
2. 90 + 46 + 44 = 180 ✓
3. 51 + 36 + 93 = 180 ✓
4. 86 + 47 + 47 = 180 ✓
5. 118 + 33 + 29 = 180 ✓
6. 42 + 64 + 74 = 180 ✓
7. 60 + 60 + 60 = 180 ✓
8. 35 + 35 + 110 = 180 ✓
9. 53 + 77 + 50 = 180 ✓

All calculations check out!

Final Answer:
1) m∠U = 80°
2) m∠B = 44°
3) m∠Q = 93°
4) m∠F = 47°
5) m∠Y = 29°
6) m∠V = 74°
7) m∠K = 60°
8) m∠U = 110°
9) m∠C = 50°