Question

IN A PARALLELOGRAM ABCD IF ANGLE A IS THRICE ANGLE B FIND ALL THE ANGLES​

Answer 1

let the four angles be x,3x,x,3x

Step-by-step explanation:

therefore x+3x+x+3x=360

8x=360

x=360/8

x = 45

Answer 2

The measure of ∠A, ∠B, ∠C and ∠D respectively are 135°, 45°, 135° and 45°

Step-by-step explanation:

We know that in a parallelogram, the opposite angles are equal

In parallelogram ABCD, the angle opposite to ∠A will be ∠C and the angle opposite to ∠B will be ∠D

Given that ∠A is thrice ∠B

Therefore,

∠A = 3∠B

or, ∠C = 3∠D

We know that in a quadrilateral, the sum of all the internal angles is 360°

Thus,

∠A + ∠B + ∠C + ∠D = 360°

or, ∠A + ∠A/3 + ∠A + ∠A/3 = 360°

or, ∠A(2+2/3) = 360°

or, 8∠A/3 = 360°

or, 8∠A/3 = 360° × 3/8 = 135°

Thus,

∠B = 135°/3 = 45°

∠C = ∠A = 135°

∠D = ∠B = 45°

Hope this answer is helpful.

Know More:

Q: In a parallelogram ABCD the measure of angle A is thrice the measure of Angle B find the measures of angle A and Angle B.

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