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 angles.

Question

Two adjacent angles of a parallelogram are (3x - 4)&#xB0; and (3x + 16)&#xB0;. Find the value of x and hence find the measure of each of its angles.

Philoid · Accepted Answer

Let ∠A = (3x - 4)°, ∠B = (3x + 16)°

Since the sum of any two adjacent angles of a parallelogram is 180°,

∠A + ∠B = 180°

(3x - 4)° + (3x + 16)° = 180°

6x + 12° = 180°

6x = 180° - 12°

6x= 168°

X= 168/6 = 28°

∠A = (3x - 4)° = 80°

∠B = (3x + 16)° = 100°

Also, ∠B + ∠C = 180° [Since, ∠B and ∠C are adjacent angles]

100° + ∠C = 180°

∠C = (180° - 100°) = 80°

Further, ∠C + ∠D = 180° [Since, ∠C and ∠D are adjacent angles]

80° + ∠D = 180°

∠D = (180° - 80°) = 100°

Therefore, x= 28°, ∠A = 80°, ∠B = 100°, ∠C = 80° and ∠D = 100°.