Question

Measure of one of the angles of a parallelogram is thrice the measure of its adjacent angle. Then angles of the parallelogram are

• A. ${60}^{\circ }$, ${30}^{\circ }$, ${120}^{\circ }$, ${150}^{\circ }$
• B. ${45}^{\circ }$, ${135}^{\circ }$, ${45}^{\circ }$, ${135}^{\circ }$
• C. ${60}^{\circ }$, ${100}^{\circ }$, ${180}^{\circ }$, ${20}^{\circ }$
• D. ${90}^{\circ }$, ${100}^{\circ }$, ${75}^{\circ }$, ${95}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$, ${135}^{\circ }$, ${45}^{\circ }$, ${135}^{\circ }$

Let the measure of the angle be $x$ and that of its adjacent angle be $y$.

$x=3y...\left(i\right)$ (given)

$x+y={180}^{\circ }...\left(ii\right)$
(sum of adjacent angles of a parallelogram is ${180}^{\circ }$)

On substituting (i) in (ii), we get

$3y+y={180}^{\circ }$

$\Rightarrow y={45}^{\circ }$

Since $x=3y$, $x={135}^{\circ }$.

We know that opposite angles of parallelogram are equal.

$\Rightarrow$ Measure of the angles are ${45}^{\circ }$, ${135}^{\circ }$, ${45}^{\circ }$ and ${135}^{\circ }$.