Question

Two adjacent angles of a parallelogram are in the ratio 4:5 . Find the measure of each of its angles bracket open hint for equal at different angles of a parallelogram are supplementary (rose

Answer 1

Answer:

A parallelogram, being a quadrilateral has four interior angles. The neighbouring angles here are consecutive angles. A diagonal splits a vertex angle into the two; those are the adjacent angles.

Two consecutive angles are supplements; one acute, the other obtuse.

By data, they are in the ratio of 4:5 = 4x:5x.

So, 4x+5x = 180°

9x = 180°

x = 20°

4x = 80° and 5x = 100°

Hence, the consecutive angles in the parallelogram are 80° and 100°.