Here are the step-by-step solutions for each problem on the worksheet. The key rule for all these problems is that the angles inside any triangle always add up to
180°.
1. This is a right-angled triangle (indicated by the square symbol at angle A), which means angle A is 90°.
* Calculation: $180^\circ - 90^\circ - 22^\circ = 68^\circ$
*
x = 68
2. The tick marks on all three sides mean this is an equilateral triangle. In an equilateral triangle, all angles are equal.
* Calculation: $180^\circ \div 3 = 60^\circ$
*
x = 60
3. The tick marks on two sides mean this is an isosceles triangle. The angles opposite the equal sides are also equal. Since angle A is 55°, angle C is also 55°.
* Calculation: $180^\circ - 55^\circ - 55^\circ = 70^\circ$
*
x = 70
4. We are given two angles: 52° and 68°.
* Calculation: $180^\circ - 52^\circ - 68^\circ = 60^\circ$
*
x = 60
5. This is a right-angled triangle (angle A is 90°). We are given angle B as 43°.
* Calculation: $180^\circ - 90^\circ - 43^\circ = 47^\circ$
*
x = 47
6. We are given two angles: 74° and 52°.
* Calculation: $180^\circ - 74^\circ - 52^\circ = 54^\circ$
*
x = 54
7. We are given two angles: 82° and 22°.
* Calculation: $180^\circ - 82^\circ - 22^\circ = 76^\circ$
*
x = 76
8. This is a right-angled triangle (angle A is 90°). We are given angle C as 64°.
* Calculation: $180^\circ - 90^\circ - 64^\circ = 26^\circ$
*
x = 26
9. We are given two angles: 54° and 49°.
* Calculation: $180^\circ - 54^\circ - 49^\circ = 77^\circ$
*
x = 77
Final Answer:
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°
Parent Tip: Review the logic above to help your child master the concept of angles of triangles worksheet answers.
