Let's solve each problem step by step using the
triangle angle sum theorem, which states:
>
The sum of the interior angles in any triangle is always 180°.
We'll use this to find the missing angle in each triangle.
---
Example (Given):
- Triangle with angles: 60°, 40°, and ∠D
- Sum = 60° + 40° + ∠D = 180°
- So, ∠D = 180° − 60° − 40° =
80°
Now let’s solve each problem:
---
1) Triangle PQR
- Right angle at Q → ∠Q = 90°
- ∠R = 30°
- Find ∠P
Calculation:
∠P = 180° − 90° − 30° =
60°
✔ Answer: ∠P = 60°
---
2) Triangle DFT
- ∠D = 50°
- ∠T = 60°
- Find ∠F
Calculation:
∠F = 180° − 50° − 60° =
70°
✔ Answer: ∠F = 70°
---
3) Triangle GHI
- ∠H = 80°
- ∠I = 30°
- Find ∠G
Calculation:
∠G = 180° − 80° − 30° =
70°
✔ Answer: ∠G = 70°
---
4) Triangle WXY
- ∠X = 60°
- ∠Y = 60°
- Find ∠W
Calculation:
∠W = 180° − 60° − 60° =
60°
✔ Answer: ∠W = 60°
(This is an equilateral triangle!)
---
5) Triangle TUV
- ∠T = 50°
- ∠U = 70°
- Find ∠V
Calculation:
∠V = 180° − 50° − 70° =
60°
✔ Answer: ∠V = 60°
---
6) Triangle ABC
- ∠A = 40°
- ∠B = 80°
- Find ∠C
Calculation:
∠C = 180° − 40° − 80° =
60°
✔ Answer: ∠C = 60°
---
7) Triangle JKL
- ∠K = 60°
- ∠L = 40°
- Find ∠J
Calculation:
∠J = 180° − 60° − 40° =
80°
✔ Answer: ∠J = 80°
---
8) Triangle PQR
- ∠P = 35°
- ∠R = 110°
- Find ∠Q
Calculation:
∠Q = 180° − 35° − 110° =
35°
✔ Answer: ∠Q = 35°
(Note: This is an isosceles triangle since two angles are equal.)
---
9) Triangle CAB
- Right angle at A → ∠A = 90°
- ∠B = 35°
- Find ∠C
Calculation:
∠C = 180° − 90° − 35° =
55°
✔ Answer: ∠C = 55°
---
✔ Final Answers:
1) ∠P =
60°
2) ∠F =
70°
3) ∠G =
70°
4) ∠W =
60°
5) ∠V =
60°
6) ∠C =
60°
7) ∠J =
80°
8) ∠Q =
35°
9) ∠C =
55°
---
🔍 Summary:
All problems were solved using:
>
Sum of interior angles = 180°
Just subtract the known angles from 180° to get the unknown one.
Let me know if you'd like a printable version or explanation for any specific triangle!
Parent Tip: Review the logic above to help your child master the concept of finding missing angles in triangles worksheet.
