Question

in the figure below, (mangle1 = 2x^{circ}) and (mangle2=(x + 63)^{circ}). 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, $2x+(x + 63)=180$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $2x+x+63 = 180$, which simplifies to $3x+63 = 180$.

Step3: Isolate the variable term

Subtract 63 from both sides: $3x+63−63=180 - 63$, resulting in $3x=117$.

Step4: Solve for $x$

Divide both sides by 3: $\frac{3x}{3}=\frac{117}{3}$, so $x = 39$.

Step5: Find $m\angle1$

Substitute $x = 39$ into the expression for $m\angle1$: $m\angle1=2x=2\times39 = 78^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 39$ into the expression for $m\angle2$: $m\angle2=x + 63=39+63 = 102^{\circ}$.

Answer:

$m\angle1 = 78^{\circ}$
$m\angle2 = 102^{\circ}$