Question

Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

Answer 1

The figure is given as follows:

It is given that two sides AB and AC of are perpendicular to sides EF and DE of respectively.

We need to prove that either or .

It's given that , thus,

Similarly,

We know that, if opposite angles of a quadrilateral are equal, then it’s a parallelogram.

Therefore,

AMEN is a parallelogram.

Also, we know that opposite angles of a parallelogram are equal.

Therefore,

By angle sum property of a quadrilateral, we have:

Hence proved.