Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle pqt = 63^{circ}$, what is $mangle utq?$

Explanation:

Step1: Identify angle - relationship

$\overleftrightarrow{PR}$ and $\overleftrightarrow{SU}$ are parallel lines and $\overleftrightarrow{VO}$ is a transversal. $\angle PQT$ and $\angle UTQ$ are alternate - interior angles.

Step2: Apply alternate - interior angles theorem

Alternate - interior angles formed by two parallel lines and a transversal are congruent. So, $m\angle UTQ=m\angle PQT$.

Answer:

$63$