Question

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

• A. ${60}^{\circ }$, ${100}^{\circ }$, ${180}^{\circ }$, ${20}^{\circ }$
• B. ${140}^{\circ }$, ${20}^{\circ }$, ${120}^{\circ }$, ${80}^{\circ }$
• C. ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$, ${120}^{\circ }$
• D. ${100}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$

Answer 1

The correct option is C

${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$, ${120}^{\circ }$

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

$x=2y...\left(i\right)$ (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

$2y+y={180}^{\circ }$

$\Rightarrow y={60}^{\circ }$

Since $x=2y$, $x={120}^{\circ }$.

We know that opposite angles of parallelogram are equal.

$\Rightarrow$ Measure of the angles are ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$ and ${120}^{\circ }$.