Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle qpn = 120^{circ}$, what is $mangle tsu$?

Explanation:

Step1: Identify corresponding angles

$\angle QPN$ and $\angle RSU$ are corresponding angles. Since $\overleftrightarrow{OQ}\parallel\overleftrightarrow{RT}$, $m\angle RSU = m\angle QPN=120^{\circ}$.

Step2: Use linear - pair relationship

$\angle RSU$ and $\angle TSU$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle RSU + m\angle TSU=180^{\circ}$.

Step3: Solve for $m\angle TSU$

$m\angle TSU=180^{\circ}-m\angle RSU$. Substitute $m\angle RSU = 120^{\circ}$ into the equation. Then $m\angle TSU = 180 - 120=60^{\circ}$.

Answer:

$60^{\circ}$