Question

in the picture, line a is parallel to line b. (mangle7 = 2x + 13) and (mangle8 = 5x+13). (x=)( angle5=)( angle6=)

Explanation:

Step1: Use vertical - angle property

Since $\angle7$ and $\angle8$ are vertical angles, they are equal. So we set up the equation $2x + 13=5x+13$.
$2x + 13=5x + 13$
$2x-5x=13 - 13$
$-3x=0$
$x = 0$

Step2: Find the measure of $\angle8$

Substitute $x = 0$ into the expression for $m\angle8$.
$m\angle8=5x + 13=5\times0+13 = 13^{\circ}$

Step3: Find $\angle5$

Since $\angle5$ and $\angle8$ are vertical angles, $m\angle5=m\angle8 = 13^{\circ}$

Step4: Find $\angle6$

$\angle6$ and $\angle8$ are supplementary (linear - pair). So $m\angle6=180 - m\angle8=180 - 13=167^{\circ}$

Answer:

$x = 0$
$\angle5=13^{\circ}$
$\angle6=167^{\circ}$