Question

$PQRS$ is a trapezium in which $PQ\parallel SR$ and $\angle P={130}^{°}$, $\angle Q={110}^{°}$. Then $\angle R$ is equal to:

• A. ${70}^{°}$
• B. ${50}^{°}$
• C. ${65}^{°}$
• D. ${55}^{°}$

Answer 1

The correct option is A

${70}^{°}$

Explanation for the correct option:

Option (a): Determine the measure of $\angle R$.

It is given that $PQRS$ is a trapezium where $PQ\parallel SR$, the measure of $\angle P={130}^{°}\mathrm{and}\angle Q={110}^{°}$.

It is known that the angle formed by a trapezium's parallel sides are supplementary.

$\begin{array}{rcl}\angle Q+\angle R& =& {180}^{°}\\ & \Rightarrow & 110+\angle R=180\\ & \Rightarrow & \angle R=180-110\\ & \Rightarrow & \angle R={70}^{°}\end{array}$

Hence, option (a) is correct.