Question

the ratio of angle A and agle B of parallelogram ABCD is 4:5,then find all the angles​

Answer 1

☆ Given :

• The ratio of angle A and B of a parallelogram ABCD is 4 : 5.

☆ To find :

• The measure of all the angles.

☆ Solution :

Let,

• ∠A = 4x
• ∠B = 5x

Thus,

we can say that,

➝ 4x + 5x = 180°

(Co-Interior angles of ||gm or sum of adjacent angles is 180° )

➝ 9x = 180°

➝ x = 180/9

➝ x = 20°

Therefore,

• ∠A = 4x = 4 × 20 = 80°
• ∠B = 5x = 5 × 20 = 100°

Hence,

∠A = ∠C = 80°

[Opposite angles of parallelogram are equal]

∠B = ∠D = 100°

[Opposite angles of parallelogram are equal]

Thus,

• All the angles of the parallelogram are :- 80°,100°,80°,100°.

Answer 2

Answer:

Let the common multiple of the given ratio then

= Angle A = 5x° and angle B = 4x°

ABCD is a parallelogram

= angle A + angle B =180° [Adjacent angle of parallelogram are supplementary]

5x + 4x = 180°

9x = 180°

x = 180/9

x = 20°

angle B = 4x = 4×20 = 80°

The measure of angle B is 80°.