Question

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

Explanation:

Step1: Recall angle - sum property

The sum of angles around a point is 360°. Also, we know that \(\angle1+\angle2 + \angle XWY=180^{\circ}\) (since they form a linear - pair or a straight - line at point \(W\)).

Step2: Substitute the given values

We are given that \(m\angle1 = 89^{\circ}\) and \(m\angle2=67^{\circ}\). Let \(m\angle XWY=x\). Then \(x + 89^{\circ}+67^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\[

$$\begin{align*} x&=180^{\circ}-(89^{\circ}+ 67^{\circ})\\ x&=180^{\circ}-156^{\circ}\\ x& = 24^{\circ} \end{align*}$$

\]

Answer:

\(24\)