Question

consider the triangle. the measures of the angles of the triangle are 32°, 53°, 95°. based on the side lengths, what are the measures of each angle? ( mangle a = 32^{circ}, mangle b = 53^{circ}, mangle c = 95^{circ} ) ( mangle a = 43^{circ}, mangle b = 32^{circ}, mangle c = 95^{circ} ) ( mangle a = 95^{circ}, mangle b = 53^{circ}, mangle c = 32^{circ} ) ( mangle a = 53^{circ}, mangle b = 95^{circ}, mangle c = 32^{circ} )

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the larger the side length, the larger the angle opposite it.

Step2: Compare the side lengths

The side lengths are \(AB = 15\), \(AC=12\), \(BC = 8\). So \(AB>AC>BC\).

Step3: Determine the angles

The angle opposite \(AB\) is \(\angle C\), the angle opposite \(AC\) is \(\angle B\), and the angle opposite \(BC\) is \(\angle A\). Since \(AB>AC>BC\), then \(m\angle C>m\angle B>m\angle A\). Given the angles \(32^{\circ}\), \(53^{\circ}\), \(95^{\circ}\), we have \(m\angle A = 32^{\circ}\), \(m\angle B=53^{\circ}\), \(m\angle C = 95^{\circ}\)

Answer:

\(m\angle A = 32^{\circ},m\angle B = 53^{\circ},m\angle C = 95^{\circ}\) (the first option)