Question

1. find m∠y

x
84°
2x + 118
w
2x + 68
z
y

Explanation:

Step1: Recall sum of angles in quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$. So, $84^{\circ}+90^{\circ}+(2x + 118)+(2x+68)=360^{\circ}$.

Step2: Combine like - terms

First, combine the constant terms and the $x$ - terms: $(2x+2x)+(84 + 90+118+68)=360$.
$4x+(84 + 90+118+68)=360$, and $84 + 90+118+68 = 360$. So, $4x+360=360$.

Step3: Solve for $x$

Subtract 360 from both sides of the equation: $4x+360 - 360=360 - 360$, which gives $4x = 0$, then $x = 0$.

Step4: Find $m\angle Y$

Substitute $x = 0$ into the expression for $\angle Y$. Since $m\angle Y=2x + 118$, then $m\angle Y=2(0)+118=118^{\circ}$.

Answer:

$118^{\circ}$