Question

Find the measure of each angle of a parallelogram whose larger angle is 30 less than twice of smaller angel

Answer 1

Let the smaller angle be a

Larger angle = 2a - 30

We know that opposite angles of parallelogram are equal,

So,

Third angle = a

Fourth angle = 2a - 30

By angle sum property of quadrilateral, we get

a + 2a - 30 + a +2a - 30 = 360

=> 6a - 60 = 360

=> 6a = 420

=> a = 70

First angle = 70°

Second angle = 110°

Third angle = 70°

Fourth angle = 110°

Answer 2

let smaller angle be c.

larger angle = 2c - 30.

sum of all four angles = 360

c + c + 2c - 30 + 2c - 30 = 360

6c -60 = 360

c = 70.

angles are 70 , 110 , 70 and 110