Question

If two straight line intersect each other in such a way that one of the angles formed measures ${90}^{\circ }$, show that each of the remaining angles measures ${90}^{\circ }$.

Answer 1

We know that if two lines intersect, then the vertically opposite angles are equal.

∠AOC = 90°. Then ∠AOC = ∠BOD = 90°

And let ∠BOC = ∠AOD = x

Also, we know that the sum of all angles in a straight line is 180°

So, $\angle AOC+\angle BOC={180}^0$

$\angle BOC=180-\angle AOC$

$\angle BOC=180-90$

$\angle BOC={90}^0$

Hence, ∠BOC = ∠AOD=90°

Therefore, ∠ AOC = ∠ BOD = ∠ BOC = ∠ AOD = 90°

Hence, the measure of each of the remaining angles are 90°.