Question

One angle of a parallelogram is twice the adjacent angle. What are the angles of the parallelogram?

• A. , , ,
• B. , , ,
• C. , , ,
• D. , , ,

Answer 1

The correct option is

A ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$ and ${120}^{\circ }$.

Let one angle be x and adjacent angle be y.
Given, x = 2y--- (i)
$\Rightarrow$ x + y = ${180}^{\circ }$---- (ii) (sum of adjacent angles of a parallelogram is ${180}^{\circ }$)
Substitute (i) in (ii), we get
y+2y=${180}^{\circ }$
3y=${180}^{\circ }$
y = ${60}^{\circ }$
$\Rightarrow$ x = 2y
$\Rightarrow$​ x = ${120}^{\circ }$
As we know that the opposite angles are equal,
So the remining angle angles are ${60}^{\circ }$ and ${120}^{\circ }$.
Therefore, the angles of given parallelogram is ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$ and ${120}^{\circ }$.