Question

the exterior angles of triangle uvw are ∠x, ∠y, and ∠z, and they are adjacent to ∠u, ∠v, and ∠w, respectively. if m∠w is 55°, and m∠y is 87°, what is m∠u? a. 125° b. 32° c. 55° d. 93°

Explanation:

Step1: Recall exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle UVW, if ∠X, ∠Y, and ∠Z are exterior angles adjacent to ∠U, ∠V, and ∠W respectively, and we want to find ∠U, and we know that the exterior angle adjacent to ∠U (let's assume it's related to the given exterior - angle information). Given an exterior angle and another non - adjacent interior angle, we use the formula: Exterior angle=Sum of non - adjacent interior angles. Let the exterior angle related to ∠U be the sum of ∠W and ∠Y.

Step2: Apply the formula

We know that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. If we assume the exterior angle related to ∠U is formed by extending one of the sides of the triangle such that the exterior angle = ∠W+∠Y. But we are given that an exterior angle (let's assume the one related to finding ∠U) and we know ∠W = 55° and ∠Y = 87°. Let the exterior angle related to ∠U be E. Then E=∠U + ∠V. Also, using the fact that the exterior angle and the non - adjacent interior angles are related. We know that if we consider the relationship for the angle we want to find. Let the exterior angle related to ∠U be the sum of the other two non - adjacent interior angles. So, ∠U=∠Y - ∠W.

Step3: Calculate the value of ∠U

Substitute the given values: ∠U=87°−55° = 32°.

Answer:

B. 32°