Question

a reflection of $\triangle qrs$ across line $n$ results in $\triangle tvu$.
what is the measure of $\angle u$?
a. $54^{\circ}$
b. $56^{\circ}$
c. $58^{\circ}$
d. $66^{\circ}$
e. $114^{\circ}$

Explanation:

Step1: Use the property of reflection

Since a reflection of $\triangle QRS$ across line $n$ results in $\triangle TVU$, then $\triangle QRS\cong\triangle TVU$.

Step2: Identify corresponding angles

In congruent triangles, corresponding angles are equal. $\angle U$ corresponds to $\angle S$.

Step3: Find the measure of $\angle U$

Given that $\angle S = 66^{\circ}$, so $\angle U=\angle S = 66^{\circ}$.

Answer:

D. $66^{\circ}$