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 the triangle angle - side relationship

In a triangle, the larger the side opposite an angle, the larger the angle. So we first identify the sides opposite each angle.

• In triangle \(WXY\), side opposite \(\angle W\) is \(XY = 10\).
• Side opposite \(\angle X\) is \(WY=14\).
• Side opposite \(\angle Y\) is \(WX = 5\).

Step2: Compare the lengths of the sides

We have the side lengths: \(WX = 5\), \(XY=10\), \(WY = 14\). So the order of the sides from shortest to longest is \(WX

Step3: Relate side lengths to angle sizes

Using the angle - side relationship:

• The angle opposite the shortest side (\(WX = 5\)) is \(\angle Y\), so \(\angle Y\) is the smallest angle.
• The angle opposite the longest side (\(WY=14\)) is \(\angle X\), so \(\angle X\) is the largest angle.
• The angle opposite \(XY = 10\) is \(\angle W\), and the angle opposite \(WX=5\) is \(\angle Y\). Since \(10>5\), \(\angle W>\angle Y\).
• The angle opposite \(WX = 5\) is \(\angle Y\) (smallest), the angle opposite \(XY = 10\) is \(\angle W\), and the angle opposite \(WY = 14\) is \(\angle X\) (largest). So \(\angle W\) is not the smallest angle, \(\angle X\) is the largest (so \(\angle X\) is not smaller than \(\angle W\)), and \(\angle Y\) is the smallest (not the largest).

Answer:

Angle W is greater than angle Y.