Two adjacent angles of a parallelogram are (3 − 4)0and (3 + 16)0. Fi

1.	Two adjacent angles of a parallelogram are (3 − 4)0and (3 + 16)0. Find the value of x and hence, find the measure of each of its angles.
Answer» 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

Two adjacent angles of a parallelogram are (3 − 4)0and (3 + 16)0. Find the value of x and hence, find the measure of each of its angles.

Answer»

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