Angles in Triangles worksheet - Free Printable

I'll solve this worksheet by finding the missing angle 'x' in each of the 9 triangles. The key principle is that the sum of all interior angles in any triangle is always 180°.

Let me go through each problem one by one:

Problem 1:
- Triangle ABC with angle B = 22°, angle A = 90° (right angle), and angle C = x
- Using the triangle angle sum: 22° + 90° + x = 180°
- So, x = 180° - 22° - 90° = 68°

Problem 2:
- This is an equilateral triangle (all sides marked equal)
- In an equilateral triangle, all angles are equal
- So, x = 180° ÷ 3 = 60°

Problem 3:
- Triangle ABC with angle A = 55°, and since two sides are marked equal (AB = BC), it's isosceles with base angles equal
- So angle C = 55°, and angle B = x
- Using the triangle angle sum: 55° + 55° + x = 180°
- So, x = 180° - 55° - 55° = 70°

Problem 4:
- Triangle ABC with angle B = 52°, angle A = 68°, and angle C = x
- Using the triangle angle sum: 52° + 68° + x = 180°
- So, x = 180° - 52° - 68° = 60°

Problem 5:
- Right triangle ABC with angle B = 43°, angle A = 90°, and angle C = x
- Using the triangle angle sum: 43° + 90° + x = 180°
- So, x = 180° - 43° - 90° = 47°

Problem 6:
- Triangle ABC with angle B = 74°, angle A = 52°, and angle C = x
- Using the triangle angle sum: 74° + 52° + x = 180°
- So, x = 180° - 74° - 52° = 54°

Problem 7:
- Triangle ABC with angle A = 82°, angle B = 22°, and angle C = x
- Using the triangle angle sum: 82° + 22° + x = 180°
- So, x = 180° - 82° - 22° = 76°

Problem 8:
- Right triangle ABC with angle C = 64°, angle A = 90°, and angle B = x
- Using the triangle angle sum: 64° + 90° + x = 180°
- So, x = 180° - 64° - 90° = 26°

Problem 9:
- Triangle ABC with angle B = 54°, angle A = 49°, and angle C = x
- Using the triangle angle sum: 54° + 49° + x = 180°
- So, x = 180° - 54° - 49° = 77°

The answers for each problem are:
1. x = 68°
2. x = 60°
3. x = 70°
4. x = 60°
5. x = 47°
6. x = 54°
7. x = 76°
8. x = 26°
9. x = 77°