Question

In a parallelogram ABCD, ∠A = (3x + 15°) and ∠B = (5x – 35°).Find the measure of ∠D.

Answer 1

∠A+∠B=180° {Sum of adjacent angles of parallelogram equals to 180°}
∴ 3x+15°+5x-35°=180°
8x-20°=180°
8x=200°
x=200°/8 
x=25°
∠D=3*25+15
∠D=90°

Answer 2

Answer:

90°

Step-by-step explanation:

Concept= Sum of Angles

Given= Measure of angle A and angle B in a parallelogram ABCD.

To Find= The unknown angle D

Explanation=

We have been provided with a parallelogram ABCD.

We have been given that ∠A= 3x+15° and ∠B= 5x-35°

So in a parallelogram we know that all four angles are there whose sum is 360°.

And the sum of adjacent angles is 180°

Here in the given parallelogram the angle A and B are adjacent to each other and the sum of adjacent angle is 180°

∠A + ∠B= 180°

3x+ 15° + 5x -35° = 180°

8x -20°= 180°

8x= 200°

x= 200/8

x= 25°

Therefore the angle A= 3x+15°= 3*25° +15°= 75° + 15° = 90°

and angle B= 5x-35= 5*25 -35= 90°

Now considering the parallelogram ∠A and ∠D are also adjacent so

∠A+∠D=180°

∠D= 180-90= 90°

Therefore the measure of ∠D is 90°.

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