Question

parallelogram properties - angles
score: 1.75/5 penalty: 0.25 off
question
in parallelogram rstu if ( mangle rst = 165^{circ} ) find ( mangle tur ).

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary. So, $m\angle RST + m\angle STU=180^{\circ}$.
Given $m\angle RST = 165^{\circ}$, then $m\angle STU=180 - 165=15^{\circ}$.

Step2: Use the property of alternate - interior angles

Since $RS\parallel TU$ and $RU$ is a transversal, $\angle TUR$ and $\angle STU$ are alternate - interior angles.
By the alternate - interior angles theorem (if two parallel lines are cut by a transversal, then alternate - interior angles are congruent), $m\angle TUR=m\angle STU$.
So, $x = 15$.

Answer:

$15$