Question

Two adjacent angles of a parallelogram are (3 − 4)

0

and (3 + 16)

0

. Find the value of x and

hence, find the measure of each of its angles.​

Answer 1

Answer: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 180o ∠A + ∠B =

180o (3x-4)o + (3x+16)o= 180o 6x + 12 = 180o 6x = 180o-12o 6x = 168o X=

168o/6 = 280 ∠A = (3x-4)o=3 × 28 – 4 =

80o ∠B

= (3x+16)o= 3 × 28 + 16 =

100o Also ∠B + ∠C = 180o [Since ∠B and ∠C are adjacent angles] 100o+ ∠C = 180o ∠C = 180o– 100o= 80o.

Now ∠C + ∠D = 180o [Since ∠C and ∠D are adjacent angles] 80o+ ∠D = 180o ∠D =

180o– 80o= 100oRead more on Sarthaks.com