Question

in the figure, (mangle7 = 100^{circ}). find the measure of (angle6).

Explanation:

Step1: Identify angle - relationship

$\angle6$ and $\angle7$ are supplementary angles.

Step2: Use supplementary - angle formula

Supplementary angles add up to $180^{\circ}$. Let $m\angle6 = x$. Then $x + m\angle7=180^{\circ}$.

Step3: Substitute the value of $m\angle7$

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

Step4: Solve for $x$

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

Answer:

$80^{\circ}$