Question

Question 30
In a parallellogram PQRS, if $\angle P={60}^{\circ }$, then other three angles are
a) ${45}^{\circ },{135}^{\circ },{120}^{\circ }$
b) ${60}^{\circ },{120}^{\circ },{120}^{\circ }$
c) ${60}^{\circ },{135}^{\circ },{135}^{\circ }$
d) ${45}^{\circ },{135}^{\circ },{135}^{\circ }$

Answer 1

Given, $\angle P={60}^{\circ }$

Since, in a parallelogram, adjacent angles are supplementary,
$\angle P+\angle Q={180}^{\circ }\Rightarrow {60}^{\circ }+\angle Q={180}^{\circ }\Rightarrow \angle Q={120}^{\circ }$
Also, opposite angles are equal in a parallelogram.
Therefore, $\angle R=\angle P={60}^{\circ },\angle S=\angle Q={120}^{\circ }$
Hence, other three angles are ${60}^{\circ },{120}^{\circ },{120}^{\circ }$.