Question

Find the angles of the parallelogram ABCD if angle C= 2/3 angle D.​

Answer 1

Given:

angle C= 2/3 angle D

To find:

All the angles of the parallelogram.

Solution:

1) In the parallelogram, the opposite angles are equal to each other.

so in parallelogram

• ∠A = ∠C = x

• ∠B = ∠D = y

2) By the angle sum property of the parallelogram,

• x+x+y+y = 360°

According to the question

x = 2y/3

• 2y/3+2y/3+y+y = 360°

• (2y+2y+3y+3y)/3 = 360°

• 10y/3 = 360°

• y = 108°

x = 2y/3

• x = 2×108/3

• x = 72°

The angles of the parallelogram are 72°, 108°, 72°, and 108°.