Question

find the measure of ∠7
given:
∠1 is a right angle
∠3 = 37°
∠8 = 62°
a 53°
b 65°
c 105°
d 127°
e 245°

Explanation:

Step1: Find the measure of ∠9

Since ∠1 is a right angle (90°) and ∠3 = 37°, in the right - angled triangle with angles ∠1, ∠3, and ∠9, we use the angle sum property of a triangle ($\angle1+\angle3+\angle9 = 180^{\circ}$).
So, $\angle9=180^{\circ}-\angle1 - \angle3$.
Substituting the values, $\angle9 = 180^{\circ}-90^{\circ}-37^{\circ}=53^{\circ}$.

Step2: Find the measure of ∠7

We know that $\angle7+\angle8+\angle9 = 180^{\circ}$ (angle - sum property of a triangle).
Given $\angle8 = 62^{\circ}$ and we found $\angle9 = 53^{\circ}$.
Then $\angle7=180^{\circ}-\angle8-\angle9$.
Substituting the values, $\angle7=180^{\circ}-62^{\circ}-53^{\circ}=65^{\circ}$.

Answer:

B. 65°