Question

In a parallelogram `square`ABCD, If ∠A = (3x + 12)°, ∠B = (2x - 32)° then find the value of x and then find the measures of ∠C and ∠D. 

Answer 1

Given: ∠A = (3x + 12)˚ and ∠B = (2x - 32)˚

Opposite angles of a parallelogram are equal.

∴ ∠C = ∠A    ...(i)

⇒ ∠C = (3x + 12)˚

∠D = ∠B        …(ii)

∠D = (2x - 32)˚

In a quadrilateral, the sum of all the angles is equal to 360˚.

∴ In `square`ABCD,

∠A + ∠B + ∠C  + ∠D = 360˚

∴ 3x + 12 + 2x - 32 + 3x + 12 + 2x - 32 = 360

∴ 10x - 40 = 360

∴ 10x = 360 + 40

∴ 10x = 400

∴ x = `400/10`

∴ x = 40

∴ ∠A = (3x + 12)˚

⇒ ∠A = 3 × 40 +12

⇒ ∠A = 120 + 12

⇒ ∠A = 132˚

∴ ∠C = 132˚        ...[From (i)]

∴ ∠B = (2x - 32)˚

⇒ ∠B = 2 × 40 - 32

⇒ ∠B = 80 - 32

⇒ ∠B = 48˚

∴ ∠D = 48˚        ...[From (ii)]

Hence, the measure of x is 40.

Also, measures of ∠C and ∠D are 132˚ and 48˚ respectively.