Question

If an angle of a parallelogram is two seventh of its adjacent angle, what is the smallest angle

of the parallelogram?​

Answer 1

Let x and y be two adjacent angles of a parallelogram.

According to the question,

$⇒ x= </p><p>3</p><p>2</p><p> </p><p> y ----- ( 1 )$

We know in parallelogram, sum of adjacent angles are supplementary.

$</p><p>∴ x+y=180 </p><p>o</p><p> .</p><p></p><p>⇒ </p><p>3</p><p>2</p><p> </p><p> y+y=180 </p><p>o</p><p> \\ [ From ( 1 ) ]</p><p> \\ </p><p>⇒ 2y+3y=540 </p><p>o</p><p> </p><p></p><p>⇒ 5y=540 </p><p>o</p><p> </p><p></p><p>⇒ y=108 </p><p>o</p><p> .$

Substituting value of y in equation ( 1 ) we get,

$⇒ x= </p><p>3</p><p>2</p><p> </p><p> ×108 </p><p>o</p><p> </p><p></p><p>⇒ x=72 </p><p>o</p><p> </p><p></p><p>$

We know that, in parallelogram opposite angles are equal.

∴ Four angles of parallelogram are

$108 </p><p>o</p><p> ,72 </p><p>o</p><p> ,108 </p><p>o</p><p> \: and \: 72 </p><p>o</p><p> .$