If an angle of a parallelogram is four-fifths of its adjacent angle, find the angles of the parallelogram.

Question

Philoid · Accepted Answer

Let ABCD be the parallelogram.

We know that opposite angles of parallelogram are equal.

∴∠A = ∠C and ∠B = ∠D
By given conditions,

Let ∠A = x° and ∠B =

Also, adjacent angles of parallelogram are supplementary,

∴ x° + = 180°

= 180°

∴ x = 100°

Hence, ∠A = 100° and ∠B = = 80°

Hence, ∠A = ∠C = 100°; ∠B = ∠D = 80°