in the figure below, (mangle1=(x + 96)^{circ}) and (mangle2 = 3x^{circ}). find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are supplementary, $(x + 96)+3x=180$.

Step2: Solve for $x$

$4x+96 = 180$, then $4x=84$, so $x = 21$.

Step3: Find angle - measures

$m\angle1=x + 96=21+96 = 117^{\circ}$, $m\angle2=3x=3\times21 = 63^{\circ}$.

Answer:

$m\angle1 = 117^{\circ}$ $m\angle2 = 63^{\circ}$