Q10 of 153 Page 118

If two straight lines intersect each other in such a way that one of the angles formed measure 90°, show that each of the remaining angles measures 90°.

Proof



Given lines AB and CD intersect each other at point O and ∠AOC = 90°


∠AOC = ∠BOD (Opposite angles)


Therefore, ∠BOD = 90°


⇒ ∠BOD + ∠AOC = 180°


⇒ ∠BOC + 90° = 180°


⇒ ∠BOC = 90°


Now, ∠AOD = ∠BOC (Opposite angles)


Therefore,


∠AOD = 90°


Proved each of the remaining angles measures 90°.


More from this chapter

All 153 →
8

In the adjoining, there coplanar lines AB, CD and EF intersect at a point O. Find the value of x. Hence, find,and .

 9

Two adjacent angles on a straight line are in the ratio 5:4 Find the measure of each one of these angles.

 11

Two lines AB and CD intersect at a point O such that + =280°, as shown in the figure. Find all the four angles.

 12

In the given figure, ray OC is the bisector of and OD is the ray opposite to OC. Show that =.