Two adjacent angles of a parallelogram are (2x+25) and (3x-5) the value of x is

Question 6 Quadrilaterals Exercise 10B

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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.

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Two adjacent angles of a parallelogram are 2x+25∘ and 3x 5∘. The value of x is a 28 b 32 c 36 d 42