Question

Q42. The measures of two adjacent angles of a parallelogram are in the ratio 4 : 5 , find the measure of each of the angles of the parallelogram. *
( a ) 80,100,80,100
( b ) 40, 50, 40, 50
( c ) 60,120 60, 120
( d ) none of these​

Answer 1

Given:-

• Measure of two adjacent angles of a parallelogram are in ratio of 4:5.

To find:-

• Measure of all angles of parallelogram.

Solution:-

Let,

First angle be 4x.

Second angle be 5x.

We know that,

Sum of two adjacent angles of parallelogram is 180°.

So,

⇒4x + 5x = 180°

⇒9x = 180°

⇒x = 180°/9

⇒x = 20°

First angle = 4x = 4×20° = 80°.

Second angle = 5x = 5×20° = 100°.

• We also know that, Opposite angles of parallelogram are equal.

So,

Angle opposite to 80° is also 80°.

Similarly,

Angle opposite to 100° is also 100°

Therefore,

First angle of parallelogram is 80°.

Second angle of parallelogram is 100°.

Third angle of parallelogram is 80°.

Fourth angle of parallelogram is 100°.