Question

for the figure shown, find ( mangle 1 ) and ( mangle 2 ).
( mangle 1=square^{circ} )

Explanation:

Step1: Find \( m\angle1 \)

Use the exterior - angle property. An exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
For the angle \( 130^{\circ} \), we have \( 130^{\circ}=m\angle1 + 77^{\circ} \).
Subtract \( 77^{\circ} \) from both sides: \( m\angle1=130^{\circ}-77^{\circ}=53^{\circ} \).

Step2: Find \( m\angle2 \)

Use the angle - sum property of a triangle. The sum of the interior angles of a triangle is \( 180^{\circ} \).
We know one angle is \( m\angle1 = 53^{\circ} \) and another is \( 16^{\circ} \). Let \( m\angle2=x \). Then \( 53^{\circ}+16^{\circ}+x = 180^{\circ} \).
First, add \( 53^{\circ}+16^{\circ}=69^{\circ} \). So, \( 69^{\circ}+x = 180^{\circ} \).
Subtract \( 69^{\circ} \) from both sides: \( x=m\angle2=180^{\circ}-69^{\circ}=111^{\circ} \).

Answer:

\( m\angle1 = 53^{\circ} \), \( m\angle2 = 111^{\circ} \)