Question

in a llgm ABCD, if angle A=(2x+25)and angle B=(3x-5), find the value of x and the measure of each angle of the llgm.​

Answer 1

Answer:

x=32

angle C=89

angleD=91

Step-by-step explanation:

adjacent angles in a parallelogram are supplementary

I.e.,sum of adjacent angles in a parallelogram=180

2x+25+3x-5=180

5x+20=180

5x=160

x=32

A=2(32)+25

A=64+25

A=89

B=3(32)-5

B=96-5

B=91

opposite angles in a parallelogram are equal

B=D,A=C

C=89

D=91

Answer 2

Question :-

In a parallelogram ABCD , if ∠A measures ( 2x + 25 ) and ∠B measures ( 3x - 5 ) . Find the value of x and also the measure of each angle of the parallelogram ?

Answer :-

Given :-

In a parallelogram ABCD , ∠A = 2x + 25 & ∠B = 3x - 5

Required to find :-

• Find the value of x & measure of each angle of parallelogram ?

Solution :-

As we know that ;

In a parallelogram, the sum of two adjacent angles is supplementary .

∠A + ∠B = 180°

since,

∠A = 2x + 25

∠B = 3x - 5

This implies ;

2x + 25 + 3x - 5 = 180°

5x + 20 = 180°

5x = 180° - 20°

5x = 160°

x = 160°/5

x = 32°

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°