Question

If an angle of a parallelogram is 4/5 of it adjacent angle, then find the measures of all the angles of the parallelogram.

Answer 1

> 80° , 100° , 80° , 100 °

Given :-

• angle of a parallelogram is 4/5 of it adjacent angle

Parallelogram property:-

1. Opposite angle are equal
2. sum of adjacent angle of parallelogram is 180°
3. sum of all angle of parallelogram is 360°

Solution:-

Suppose a parallelogram ABCD

let,the angle B be x

it is given that,

an angle of a parallelogram is 4/5 of it adjacent angle,

therefore,

A = 4/5B

or,

A = 4/5x

we know that,

A = C and,

B = D ( property of parallelogram)

•°• A= 4/5x , B = x , C = 4/5x , D = x

Sum of all angle of parallelogram is 360°

A + B + C + D = 360°

= 4/5x + x + 4/5x + x = 360

= 8/5x + 2x = 360

= (8x+ 10x)/5 = 360

= 18x = 360 x 5

= x = 360 x 5 / 18

= x = 100

Hence,

A = 4/5x = 4/5x100 = 80°

B = x = 100°

C = A = 80°

D = B = 100°

⚽ Verification ⚽

100 + 80 + 100 + 80 = 360°

Hence, verified ✔️