Question

Question 133
Two adjacent angles of a parallelogram are in the ratio 1 : 3. Find its angles.

Answer 1

Let the adjacent angles of the parallelogram be x and 3x.

Then, we have $x+3x={180}^{\circ }$ [$\because$ adjacent angles of parallelogram are supplementary]
$\Rightarrow 4x={180}^{\circ }\Rightarrow x={45}^{\circ }$
Thus, the adjacent angles are ${45}^{\circ },{135}^{\circ }$.
Hence, the angles are ${45}^{\circ },{135}^{\circ },{45}^{\circ },{135}^{\circ }$. [$\because$ opposite angles in a parallelogram are equal].