Question

in the figure below, \\( \triangle stu \\) is congruent to \\( \triangle vwu \\).

if \\( m\angle uwv = 39 ^ { \circ } \\) and \\( m\angle wuv = 119 ^ { \circ } \\), what is the measure of \\( \angle ust \\)?

a. \\( 68 ^ { \circ } \\)
b. \\( 22 ^ { \circ } \\)
c. \\( 51 ^ { \circ } \\)
d. \\( 23 ^ { \circ } \\)

Explanation:

Step1: Find the measure of ∠VWU

Use the angle - sum property of a triangle ($\angle VWU+\angle UWV+\angle WUV = 180^{\circ}$).
$$\angle VWU=180^{\circ}-\angle UWV - \angle WUV$$
Substitute $\angle UWV = 39^{\circ}$ and $\angle WUV = 119^{\circ}$.
$$\angle VWU=180^{\circ}-39^{\circ}-119^{\circ}=22^{\circ}$$

Step2: Use the congruence of triangles

Since $\triangle STU\cong\triangle VWU$, corresponding angles are equal. $\angle UST=\angle VWU$.

Answer:

B. \(22^{\circ}\)