Question

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 (form a straight - line), we have $(x + 96)+3x=180$.

Step2: Combine like terms

Combining the $x$ terms gives $4x+96 = 180$.

Step3: Isolate variable

Subtract 96 from both sides: $4x=180 - 96$, so $4x=84$.

Step4: Solve for x

Divide both sides by 4: $x=\frac{84}{4}=21$.

Step5: Find angle measures

For $\angle1$, substitute $x = 21$ into $m\angle1=(x + 96)^{\circ}$, so $m\angle1=(21 + 96)^{\circ}=117^{\circ}$.
For $\angle2$, substitute $x = 21$ into $m\angle2 = 3x^{\circ}$, so $m\angle2=3\times21^{\circ}=63^{\circ}$.

Answer:

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