Question

In a parallelogram ABCD, if ∠= (3 − 12)°, ∠ = 2 − 32 °,find the value of .​

Answer 1

Answer:

i. ABCD is a parallelogram. [Given] ∴ ∠A + ∠B = 180° [Adjacent angles of a parallelogram are supplementary], ∴ (3x + 12)° + (2x-32)° = 180° ∴ 3x + 12 + 2x – 32 = 180 ∴ 5x – 20 = 180 ∴ 5x = 180 + 20 ∴ 5x = 200 ∴ x = 200/5 ∴ x = 40

ii. ∠A = (3x + 12)° = [3(40) + 12]° = (120 + 12)° = 132° ∠B = (2x – 32)° = [2(40) – 32]° = (80 – 32)° = 48° ∴ ∠C = ∠A = 132° ∠D = ∠B = 48° [Opposite angles of a parallelogram]

∴ The value of x is 40, and the measures of ∠C and ∠D are 132° and 48° respectively.

Answer 2

Answer:

Answer

∠A=3x+12

∠B=2x−32

Now sum of adjacent angles of a parallelogram is 180.

⇒3x+12+2x−32=180

⇒5x−20=180

⇒5x=200

⇒x=40

∠A=3(40)+12=132

∠B=2(40)−32=48

Now opposite angles in a parallelogram are equal

⇒∠A=∠C and ∠B=∠D

∴∠C=132 and ∠D=48.