Question

Two adjacent angles of a parallelogram are (3x-4)° and (3x+16)°. Find the value of x and hence find the measure of each of its angle.

Answer 1

Let ∠A = (3x-4)^o and ∠B = (3x+16)^o

Let ∠A and ∠B are two adjacent angles.

But we know that sum of adjacent angles of a parallelogram is 180^o

∠A + ∠B = 180^o

(3x-4)^o + (3x+16)^o= 180^o

6x + 12 = 180^o

6x = 180^o-12^o

6x = 168^o

X= 168^o/6 = 28⁰

∠A = (3x-4)^o=3 × 28 – 4 = 80^o

∠B = (3x+16)^o= 3 × 28 + 16 = 100^o

Also ∠B + ∠C = 180^o [Since ∠B and ∠C are adjacent angles]

100^o+ ∠C = 180^o

∠C = 180^o– 100^o= 80^o.

Now ∠C + ∠D = 180^o [Since ∠C and ∠D are adjacent angles]

80^o+ ∠D = 180^o

∠D = 180^o– 80^o= 100^o