Question

ABCD is a parallelogram angle B= 5x+25 and angle D = 8x-5 find x and angle C ​

Answer 1

Answer:

Step-by-step explanation:

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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Answer 2

Answer:

Angle B = Angle D (Opposite Angles of parallelogram)

5x + 25 = 8x – 5

25 + 5 = 8x – 5x

30 = 3x

x = 30/3

x = 10

Angle B = 5x + 25 = 5(10)+25 = 75°

Angle B + Angle C = 180° (Co-Interior Angles)

75° + Angle C = 180°

Angle C = 180° – 75°

Angle C = 105°

So, x = 10 and Angle C = 105°.