Question

(2x + 35
А
2. In a parallelogram ABCD, if ZA = (2x + 35) and ZC = (3x - 5).
Find : (i) the value of x (ii) measure of each angle of ABCD.
(Hint: ZA = ZC, ZB = ZD and ZA + B + ZC + ZD = 360°.)​

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°