Question

In figure, $\overline{ST}$ and $\overline{QR}$ are parallel, $\overline{RU}$ and $\overline{QT}$ are perpendicular, $\angle RQU=x+4$, and $m\angle QTS=2x-30$. Calculate the measure of $\angle QRU$.

• A. ${34}^{\circ }$
• B. ${38}^{\circ }$
• C. ${52}^{\circ }$
• D. ${68}^{\circ }$
• E. ${88}^{\circ }$

Answer 1

The correct option is C ${52}^{\circ }$

Given $ST$ and $QR$ are parallel, $RU$ and $QT$ are perpendicular.

$\angle RQU=x+4$ and $\angle QST=2x-30$

Given $ST$ and $QR$ are parallel and line $QT$ cut both lines.

Then $\angle QST=\angle RQU$

$\therefore 2x-30=x+4$

$\Rightarrow 2x-x=4+30$

$\Rightarrow x=34$

Then $\angle RQU=34+4={38}^0$

In $\Delta QUR$

Then $\angle QRU+\angle RQU+\angle QUR=180$

$\therefore QRU=180-38+90={52}^0$