Question

in the figure below, m∠1=(x + 96)° and m∠2 = 3x°. find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are supplementary (form a straight - line), $m\angle1 + m\angle2=180^{\circ}$. So, $(x + 96)+3x=180$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $4x+96 = 180$.

Step3: Isolate the 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 $m\angle1$

Substitute $x = 21$ into the expression for $m\angle1$: $m\angle1=(x + 96)^{\circ}=(21+96)^{\circ}=117^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 21$ into the expression for $m\angle2$: $m\angle2=3x^{\circ}=3\times21^{\circ}=63^{\circ}$.

Answer:

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