Question

in the figure below, m∠1=(x + 24)° and m∠2 = 3x°. find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are supplementary (linear - pair of angles), $m\angle1 + m\angle2=180^{\circ}$. So, $(x + 24)+3x=180$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $4x+24 = 180$.

Step3: Isolate the variable term

Subtract 24 from both sides: $4x=180 - 24$, so $4x=156$.

Step4: Solve for $x$

Divide both sides by 4: $x=\frac{156}{4}=39$.

Step5: Find $m\angle1$

Substitute $x = 39$ into the expression for $m\angle1$: $m\angle1=(x + 24)^{\circ}=(39+24)^{\circ}=63^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 39$ into the expression for $m\angle2$: $m\angle2=3x^{\circ}=3\times39^{\circ}=117^{\circ}$.

Answer:

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