Question

in the figure below, (mangle4 = 77^{circ}). find (mangle1), (mangle2), and (mangle3).

Explanation:

Step1: Vertical - angles are equal

$m\angle1 = m\angle3$

Step2: Supplementary - angles

$m\angle1 + m\angle4=180^{\circ}$, so $m\angle1 = 180 - 77=103^{\circ}$

Step3: Vertical - angles

$m\angle2 = m\angle4 = 77^{\circ}$

Answer:

$m\angle1 = 103^{\circ}$
$m\angle2 = 77^{\circ}$
$m\angle3 = 103^{\circ}$