Question

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

Explanation:

Step1: Recall angle - sum property

The sum of angles around a point is 360°. Also, assume the angle we want to find is \(m\angle XWY\), and we know \(m\angle1 = 89^{\circ}\) and \(m\angle2=67^{\circ}\). And \(\angle1+\angle2 + m\angle XWY=180^{\circ}\) (since they form a straight - line or a linear pair).

Step2: Solve for \(m\angle XWY\)

We can use the formula \(m\angle XWY=180^{\circ}-(m\angle1 + m\angle2)\). Substitute \(m\angle1 = 89^{\circ}\) and \(m\angle2 = 67^{\circ}\) into the formula. So \(m\angle XWY=180-(89 + 67)\). First, calculate \(89+67 = 156\). Then \(m\angle XWY=180 - 156=24^{\circ}\).

Answer:

\(24\)