Answer:
m∠C = 117°
Explanation:
If two triangles are similar, their corresponding angles are the same size.
If ΔABC ~ ΔDEF then:
- m∠A = m∠D
- m∠B = m∠E
- m∠C = m∠F
As m∠A = 52° and m∠E = 11° then:
- m∠A = m∠D = 52°
- m∠B = m∠E = 11°
- m∠C = m∠F
Interior angles of a triangle sum to 180°.
Therefore:
⇒ m∠A + m∠B + m∠C = 180°
⇒ 52° + 11° + m∠C = 180°
⇒ 63° + m∠C = 180°
⇒ 63° + m∠C - 63° = 180° - 63°
⇒ m∠C = 117°
Therefore, the measure of angle C is 117°.