Question

in the figure, (mangle7 = 100^{circ}). find the measure of (angle8).

Explanation:

Step1: Identify angle - relationship

$\angle7$ and $\angle8$ are supplementary angles (linear - pair).

Step2: Use the supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. Let $m\angle8=x$. Then $m\angle7 + x=180^{\circ}$.

Step3: Substitute the value of $m\angle7$

Given $m\angle7 = 100^{\circ}$, we have $100^{\circ}+x = 180^{\circ}$.

Step4: Solve for $x$

$x=180^{\circ}-100^{\circ}=80^{\circ}$.

Answer:

$80^{\circ}$