Question

1. find all missing angles.

1
72°
57°
3
2
4
57
72
51
75

Explanation:

Step1: Find angle 2

Since the large - triangle has a right - angle (90°) and one angle is 72°, in a triangle the sum of interior angles is 180°. So, $\angle2=90^{\circ}-72^{\circ}=18^{\circ}$.

Step2: Find angle 3

In the small triangle, we know one angle is 57° and $\angle2 = 18^{\circ}$. Using the angle - sum property of a triangle ($180^{\circ}$), $\angle3=180^{\circ}-(57^{\circ}+18^{\circ})=105^{\circ}$.

Step3: Find angle 1

In the large triangle, $\angle1 = 180^{\circ}-(90^{\circ}+72^{\circ}) = 18^{\circ}$.

Step4: Find angle 4

$\angle4=180^{\circ}-\angle3=180^{\circ}-105^{\circ}=75^{\circ}$

Answer:

75