Question

in a parallelogram ABCD,if angle A = (2x+35) and angle C = (3x - 5).Find the value of x and the measure of each angle

Answer 1

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°

Answer 2

Answer:

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