Question

In a parallelogram ABCD, angle C=(3x-5) and angle D=(2x+15) then value of x is (a)32 (b)30 (c)42 (d)34​

Answer 1

Answer:

Step-by-step explanation:

angle c and d are adjacent angles so their sum will be 180

3x-5 + 2x+15 = 180

5x + 10 = 180

5x=170

x=34

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Answer 2

Given : In a parallelogram ∠A =(2x + 35), ∠C= (3x - 5)

To find : Value of x, m∠A , m∠B , m∠C, m∠D=?

Solution:

Quadrilateral ABCD is A parallelogram.

∴∠A=∠C .........Opposite angles of parallelogram

∴ 2x + 35 = 3x - 5

∴ 35 + 5 = 3x - 2x

∴ 40 = x

∴ x = 40

∴∠A = ∠C = 2x + 35

                   = 2 x 40 +35

                   = 80 + 35

 ∴ ∠A= ∠C = 115°

Adjacent angles of parallelogram are Supplementary

∴ ∠A + ∠B = 180°

∴ 115 + ∠B = 180

∴ ∠B = 180 - 115

∴ ∠B = 65°

∠B = ∠D = 65°.......Opposite angles of parallelogram.

∴ X = 40

∴m∠A = m∠C = 115°

∴m∠B = m∠D = 65°

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