Question

in the picture, line a is parallel to line b. m∠4 = 9x - 5 and m∠5 = 4x + 16 x =
∠3 =
∠6 =

Explanation:

Step1: Use alternate - interior angles property

Since line $a$ is parallel to line $b$, $\angle4$ and $\angle5$ are alternate - interior angles and are congruent. So we set up the equation $9x - 5=4x + 16$.
$9x-4x=16 + 5$
$5x=21$
$x=\frac{21}{5}=4.2$

Step2: Find the measure of $\angle3$

$\angle3$ and $\angle4$ are supplementary (linear - pair). First, find $m\angle4$: $m\angle4=9x - 5=9\times4.2-5=37.8 - 5 = 32.8$. Then $m\angle3 = 180 - m\angle4=180 - 32.8 = 147.2$

Step3: Find the measure of $\angle6$

$\angle6$ and $\angle5$ are vertical angles, so they are congruent. First, find $m\angle5$: $m\angle5=4x + 16=4\times4.2+16=16.8 + 16 = 32.8$. So $m\angle6 = 32.8$

Answer:

$x = 4.2$
$\angle3=147.2$
$\angle6 = 32.8$