Question

One angle of a parallelogram is twice its adjacent angle. Find the measure of all the 4 angles of the parallelogram.

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

Answer 1

The correct option is C

, , ,

Let one angle be x and the 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

$\Rightarrow$ 2y + y = ${180}^{\circ }$
$\Rightarrow$ y = ${60}^{\circ }$
$\Rightarrow$ x = 2y
$\Rightarrow$​ x = ${120}^{\circ }$

So, 4 angles of the given parallelogram are ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$ and ${120}^{\circ }$.