Question

look at this diagram: if $overleftrightarrow{qs}$ and $overleftrightarrow{tv}$ are parallel lines and $mangle sru = 66^{circ}$, what is $mangle tur$?

Explanation:

Step1: Identify angle - relationship

$\angle SRU$ and $\angle TUR$ are same - side interior angles.

Step2: Apply property of parallel lines

When two parallel lines are cut by a transversal, same - side interior angles are supplementary, i.e., their sum is $180^{\circ}$. So $m\angle SRU + m\angle TUR=180^{\circ}$.

Step3: Solve for $m\angle TUR$

Given $m\angle SRU = 66^{\circ}$, then $m\angle TUR=180^{\circ}-m\angle SRU$. Substitute $m\angle SRU = 66^{\circ}$ into the equation: $m\angle TUR = 180 - 66=114^{\circ}$.

Answer:

$114$