Question

δefg ~ δyxz. what is m∠e?
(there are two triangles: δefg with ∠g = 72°, and δyxz with ∠x = 39°, ∠y = 69°)
m∠e = □°

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle EFG\sim\triangle YXZ\), corresponding angles are equal.

Step2: Calculate the measure of \(\angle E\)

We know that the sum of angles in a triangle is \(180^{\circ}\). In \(\triangle YXZ\), \(\angle X = 39^{\circ}\), \(\angle Y=69^{\circ}\). Let \(\angle Z\) be the third angle. Then \(\angle Z=180^{\circ}-(39^{\circ} + 69^{\circ})=180^{\circ}-108^{\circ} = 72^{\circ}\).
In \(\triangle EFG\), \(\angle G = 72^{\circ}\). Let \(\angle E\) and \(\angle F\) be the other two angles.
Since \(\triangle EFG\sim\triangle YXZ\), \(\angle E\) corresponds to \(\angle Z\) (by the order of similarity \(\triangle EFG\sim\triangle YXZ\), \(E\) - \(Z\), \(F\) - \(X\), \(G\) - \(Y\)).

Answer:

\(72\)