Question

Find the missing angle.

Answer 1

Answer:

$m\angle XYV=135^{\circ}$

Step-by-step explanation:

Notice that $m\angle XYV=m\angle XYW+m\angle VYW$.

The diagram already marks $m\angle VYW=80^{\circ}$, so we just need to find $m\angle XYW$.

$\angle TYU$ and $\angle XYW$ are vertical angles, which means they are equal in measure.

Therefore,

$m\angle TYU=m\angle XYW=6x+7$

Since there are $180^{\circ}$ on each side of a line, we have the following equation:

$m\angle XYW+m\angle VYW+m\angle UYV=180^{\circ},\\6x+7+13+4x+80=180,\\10x+20=100,\\10x=80,\\x=8$.

Plugging in $x=8$, we have:

$m\angle XYW=6(8)+7=55^{\circ}$.

Therefore,

$m\angle XYV=55^{\circ}+80^{\circ},\\m\angle XYV=\fbox{ 135^{\circ} }$.