Question

In a parallelogram ABCD, If angle A= (3x + 12), angle B = (2x - 32)º then find the value of X and then find the measures of angle C and angle D


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Answer 1

Answer:

We know that the opposite angles are equal in a parallelogram

Consider parallelogram ABCD

So we get

∠ A = ∠ C = (2x + 25)

∠ B = ∠ D = (3x - 5)

We know that the sum of all the angles of a parallelogram is 360

So it can be written as

∠ A + ∠ B + ∠ C + ∠ D = 360

By substituting the values in the above equation

(2x + 25) + (3x – 5) + (2x + 25) + (3x – 5) = 360

By addition we get

10x + 40 = 360

By subtraction

10x = 360 - 40

So we get

10x = 320

By division we get

x = 32

Now substituting the value of x

∠ A = ∠ C = (2x + 25) = (2(32) + 25)

∠ A = ∠ C = (64 + 25)

By addition

∠ A = ∠ C = 89

∠ B = ∠ D = (3x - 5) = (3(32) - 5)

∠ B = ∠ D = (96 - 5)

By subtraction

∠ B = ∠ D = 91

Therefore, x = 32, ∠ A = ∠ C = 89 and ∠ B = ∠ D = 91.

Answer 2

∠A=(3x+12)

o

∠B=(2x−32)

o

Now sum of adjacent angles of a parallelogram is 180

o

.

⇒∠A+∠B=180

o

⇒3x+12+2x−32=180

⇒5x−20=180

⇒5x=200

⇒x=40

So

∠A=(3(40)+12)

o

=132

o

∠B=(2(40)−32)

o

=48

o

Now opposite angles in a parallelogram are equal

⇒∠A=∠C and ∠B=∠D

∴∠C=132

o

and ∠D=48

o

.

Two angles of a parallelogram are (3x + 12) and (2x - 32).

We know that the sum of adjacent angles of a parallelogram is 180. = > x = 40.