Question

(d)The adjacent angles of a parallelogram are as 2:3. Find the measures of all its angles.​

Answer 1

Step-by-step explanation:

Let the ratio be x

now we have, 2x and 3x

In a parallelogram we know that opposite sides are parallel.

so now we have, 2x , 3x, 2x, 3x

now by using exterior angle property

2x+3x+2x+3x = 360

10x = 360

x = 360/10

x= 36

2x = 72

3x = 108

Answer 2

adjacent angles of a parallelogram are supplementary

2x + 3x = 180

5x=180

x=180/5

x=36°

thus,

2x=2×36

=72°

3x=3×36

=108°

we also know that opposite angles are equal in a parallelogram so, the measures of all the angles 72°,108°,72°,108°

verification -

the sum of all the angles in a quadrilateral =360°

72°+108°+72°+108°=360°