Question

If one of the 4 angle formed by two intersecting lines is a right angle then show the 4 angles are equal

Answer 1

so one angle is 90 its opposite is 90 too vertically opposite angle. Hence other two angles are 90 too

Answer 2

Suppose PQ and RS are two lines intersecting each other at O.

Then, four angles are POR, QOR, QOS and POS.

And POR and QOR are a vertically opposite angle pair. Similary QOS and POS are a vertically opposite angle pair.

Given that One angle POR = 90

Since, vertically opposite angles are equal. [Property of intersecting lines]

Then QOS = 90

Now POR and QOR are a linear pair of angles.

Then POR+QOR=180

Therefore, QOR = 90

If, QOR =90 then it's vertically opposite anle POS = 90

Hence proved that POR=QOR=QOS=POS=90