Question

consider triangle wxy. which statement about the angles is true? angle w is greater than angle y. angle y is the largest angle. angle x is smaller than angle w. angle w is the smallest angle.

Explanation:

Step1: Recall angle - side relationship

In a triangle, the largest angle is opposite the longest side and the smallest angle is opposite the shortest side.

Step2: Identify side lengths

In triangle \(WXY\), the side lengths are \(WX = 5\), \(XY=10\), and \(WY = 14\).

Step3: Determine angle - side correspondence

The angle opposite \(WX\) is \(Y\), the angle opposite \(XY\) is \(W\), and the angle opposite \(WY\) is \(X\). Since \(WX\) is the shortest side, angle \(Y\) is the smallest angle. Since \(WY\) is the longest side, angle \(X\) is the largest angle. And since \(XY\) is the middle - length side, angle \(W\) is the middle - sized angle. So, angle \(W\) is greater than angle \(Y\).

Answer:

Angle W is greater than angle Y.