Question

If two adjacent angles of a parallelogram are in the ratio $2:3,$then the measure of angles are

• A. $72°,108°$
• B. $36°,54°$
• C. $80°,120°$
• D. $96°,144°$

Answer 1

The correct option is A

$72°,108°$

Solve for the value of two adjacent angles.

Sum of adjacent angles of a parallelogram $=180°$

Let us assume two angles be $2n$ and $3n$ because the two angles are in the ratio $2:3.$

Then,

$\Rightarrow$$2n+3n=180°$

$\Rightarrow$ $5n=180$

$\Rightarrow$ $n=\frac{180}{5}$

$\Rightarrow$ $n=36°$

Therefore the two angles are

$\Rightarrow$$2n=2\times 36=72°$

$\Rightarrow$$3n=3\times 36=108°$

Hence the correct option is option(A)