If one angle of a parallelogram is 24° less than twice the smallest angle then the largest angle of the parallelogram is

Question

If one angle of a parallelogram is 24&#xB0; less than twice the smallest angle then the largest angle of the parallelogram is

Philoid · Accepted Answer

Let ∠A = x°,

∠B = (2x – 24)°

∠C = x° (Opposite angles are equal.)

∠D = (2x – 24)° (Opposite angles are equal.)

Since the sum of angles of a parallelogram is 360°,

∠A + ∠B + ∠C + ∠D = 360°

x° + (2x – 24)° + x° + (2x – 24)° = 360°

6x° – 48 =360°

6x° = 408°

x° = 68°

∠A = 68°

∠B = (2x – 24)° = 112°

Therefore, largest angle of the parallelogram is 112°.