Question

in a parallelogram ABCD, 3 angle A = angle D
Find the measure of all angles of a
the parallelogram ​

Answer 1

Answer:

3∠A = ∠D

∠A + ∠D = 180°         [Adjacent angles of a parallelogram are supplementary]

⇒∠A + 3∠A = 180°

⇒4∠A = 180°

⇒∠A = 45°

∠D = 3∠A = 135°

∠A = ∠C = 45°                          [Opposite angles of a parallelogram are equal]

and, ∠B = ∠D = 135°                 [Opposite angles of a parallelogram are equal]

I hope that it helps

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Answer 2

In parallelogram ABCD,

Let ∠A be x. Then, ∠B will be 2x−15

We know that, in a parallelogram sum of adjacent angles are supplementary.

∴ ∠A+∠B=180

⇒ x+2x−15 =180

⇒ 3x=195

⇒ x=65

∴ ∠A=65

⇒ ∠B=2x−15 =2×65 −15 =115

We know that, in parallelogram opposite angles are equal.

∴ ∠A=∠C and ∠B=∠D

∴ ∠C=65 and ∠D=115

∴ The measure of all angles of a parallelogram are 65 ,115 ,65 and 115 .

Put degree sign everywhere .