Question

Question 31
If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measures of the angles are
a) ${72}^{\circ },{108}^{\circ }$
b) ${36}^{\circ },{54}^{\circ }$
c) ${80}^{\circ },{120}^{\circ }$
d) ${96}^{\circ },{144}^{\circ }$

Answer 1

Given, two adjacent angles of a parallelogram are in the ratio 2 : 3
Let the angles be 2x and 3x.
Then,
$2x+3x={180}^{\circ }$ [$\because$ adjacent angles of a parallelogram are supplementary]
$\Rightarrow 5x={180}^{\circ }\Rightarrow x={36}^{\circ }$
Hence, the measures of the angles are $2x=2\times {36}^{\circ }={72}^{\circ }$ and $3x=3\times {36}^{\circ }={108}^{\circ }$.