Let's solve each triangle problem step by step using the
Triangle Angle Sum Theorem, which states:
>
The sum of the interior angles of a triangle is always 180°.
We will use:
$$
\angle A + \angle B + \angle C = 180^\circ
$$
---
1) Triangle PQR
- Given: ∠Q = 90°, ∠R = 40°
- Find: ∠P
$$
∠P = 180^\circ - 90^\circ - 40^\circ = 50^\circ
$$
✔ ∠P = 50°
---
2) Triangle DEF
- Given: ∠D = 35°, ∠F = 40°
- Find: ∠E
$$
∠E = 180^\circ - 35^\circ - 40^\circ = 105^\circ
$$
✔ ∠E = 105°
---
3) Triangle GHI
- Given: ∠H = 65°, ∠I = 65°
- Find: ∠G
$$
∠G = 180^\circ - 65^\circ - 65^\circ = 50^\circ
$$
✔ ∠G = 50°
---
4) Triangle WXY
- Given: ∠X = 70°, ∠Y = 65°
- Find: ∠W
$$
∠W = 180^\circ - 70^\circ - 65^\circ = 45^\circ
$$
✔ ∠W = 45°
---
5) Triangle TUV
- Given: ∠T = 100°, ∠V = 45°
- Find: ∠U
$$
∠U = 180^\circ - 100^\circ - 45^\circ = 35^\circ
$$
✔ ∠U = 35°
---
6) Triangle ABC
- Given: ∠A = 70°, ∠B = 60°
- Find: ∠C
$$
∠C = 180^\circ - 70^\circ - 60^\circ = 50^\circ
$$
✔ ∠C = 50°
---
7) Triangle JKL
- Given: ∠K = 105°, ∠L = 40°
- Find: ∠J
$$
∠J = 180^\circ - 105^\circ - 40^\circ = 35^\circ
$$
✔ ∠J = 35°
---
8) Triangle PQR
- Given: ∠P = 35°, ∠R = 110°
- Find: ∠Q
$$
∠Q = 180^\circ - 35^\circ - 110^\circ = 35^\circ
$$
✔ ∠Q = 35°
---
9) Triangle CBT
- Given: ∠B = 50°, ∠T = 90° (right angle)
- Find: ∠C
$$
∠C = 180^\circ - 50^\circ - 90^\circ = 40^\circ
$$
✔ ∠C = 40°
---
✔ Final Answers:
1) ∠P =
50°
2) ∠E =
105°
3) ∠G =
50°
4) ∠W =
45°
5) ∠U =
35°
6) ∠C =
50°
7) ∠J =
35°
8) ∠Q =
35°
9) ∠C =
40°
---
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of triangle angles worksheet.
