Answer:
13. The measure of a is 35°
14. The measure of b is 74°
15. The measure of c is 66°
Step-by-step explanation:
In the given figure
13.
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ 33° + 112° + a = 180°
→ Add the like terms in the left side
∴ 145° + a = 180
→ Subtract 145° from both sides
∵ 145° - 145° + a = 180° - 145°
∴ a = 35°
14.
∵ a, 71° and b formed a straight line
∵ The sum of the measures of the linear angles is 180°
∴ a + 71° + b = 180°
→ Substitute the value of a
∴ 35° + 71° + b = 180°
→ Add the like terms in the left side
∴ 106° + b = 180°
→ Subtract 106° from both sides
∵ 106° - 106° + b = 180° - 106°
∴ b = 74°
15.
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ 43° + 71° + c = 180°
→ Add the like terms in the left side
∴ 114° + c = 180°
→ Subtract 114° from both sides
∵ 114° - 114° + c = 180° - 114°
∴ c = 66°
