Question

In a IIgm ABCD , if angle A = ( 2x+25)° and angle B = (3x - 5)°, find the value of x and the measure of each angle of the parallelogram ​

Answer 1

Answer:

∠ A +∠ B=180° (corresponding angle are 180º.)

2x+25+3x-5=180º ( angle A=2x+25 and angle B=3x-5)

5x+20=180º

5x=(180-20)º

x=(160÷5)º

x=32º

So,

Measurement of ∠A = 2x + 25

=> 2 ( 32 ) + 25

=> 64 + 25

=> 89°

Measurement of ∠B = 3x - 5

=> 3 ( 32 ) - 5

=> 96 - 5

=> 91°

Hence,

∠A = 89° & ∠B = 91°

Similarly ,

In a parallelogram , opposite angles are also equal .

So,

∠A = ∠C

[ Reason : Opposite angles are equal ]

=> ∠C = 89°

∠B = ∠D

[ Reason : Opposite angles are equal ]

=> ∠D = 91°

Therefore,

Measurements of the angles are ;

∠A = 89° , ∠B = 91° , ∠C = 89° & ∠D = 91°