Question

in the figure below, m∠1 = 89° and m∠2 = 67°. find m∠xwy.

Explanation:

Step1: Identify angle - sum relationship

The sum of angles around a point is 360°. Here, $\angle 1$, $\angle 2$ and $\angle XWY$ are angles around point $W$. So, $m\angle1 + m\angle2+m\angle XWY= 180^{\circ}$ (since they form a straight - line pair of angles).

Step2: Rearrange for $m\angle XWY$

$m\angle XWY=180^{\circ}-(m\angle1 + m\angle2)$.
Substitute $m\angle1 = 89^{\circ}$ and $m\angle2 = 67^{\circ}$ into the formula.
$m\angle XWY=180-(89 + 67)$.
First, calculate the sum inside the parentheses: $89+67 = 156$.
Then, $m\angle XWY=180 - 156$.
$m\angle XWY = 24^{\circ}$.

Answer:

$24$