Question

Two adjacent angles of a parallelogram PQRS are in ratio 2:7. Find all the angles of the parallelogram.

Answer 1

let the ratio be x
sum of all angles = 360
opposite angles are equal in para...
so we have
2x +2x +7x +7x =360
18x=360
x = 20

Answer 2

The angles of the parallelogram are 40° , 140° , 40° and 140°.

• Two adjacent angles of a parallelogram PQRS are in ratio 2:7.

• Let suppose, ∠P:∠Q = 2:7
• Let the common multiple be x.
• Therefore, ∠P=2x and ∠Q=7x.
• Opposite angles of a parallelogram are congruent.
• Therefore, ∠R=2x and ∠S=7x.
• Now sum of all angles of a quadrilateral is equal to 360°.

∠P + ∠Q + ∠R + ∠S = 360

2x + 7x + 2x + 7x = 360

18x = 360

x = 20

• Now, ∠P = 2×20 = 40° , ∠Q = 7×20=140°, ∠R =40° and ∠S=140°