Question

For the given diagram if the value of $\angle 2={108}^{\circ }$, then for $CD$ parallel to $PQ$, $\angle 5=$.

• A. ${72}^{\circ }$
• B. ${108}^{\circ }$
• C. ${252}^{\circ }$

Answer 1

The correct option is A ${72}^{\circ }$

Given $\angle 2={108}^{\circ }$.
$\angle 2$ and $\angle 3$ are a linear pair.
$\Rightarrow \angle 3={180}^{\circ }-{108}^{\circ }={72}^{\circ }$
Now, $\angle 3$ and $\angle 5$ are alternate interior angle.
If $CD$ amd $PQ$ are parallel to each other.
$\Rightarrow \angle 3=\angle 5={72}^{\circ }$