Question

4. Draw two intersecting lines such that one of the angles thus formed is 70°. Find the
measure of the remaining angles formed.​

Answer 1

Answer:

Step-by-step explanation:

Two straight lines intersect each other in such a way that one of the formed angles is 90°.

To find,

Remaining angles are also 90°.

Solution,

Let,the two straight lines = AB and CD

And, their intersection point = O

According,to the data mentioned in the question one of the formed angles is 90°. We marked that 90° angle as ∠BOC. (Shown in diagram below.)

Other three angles are = ∠AOC,∠AOD and ∠BOD.

Now,AB is a straight line. So,the ∠AOB will be 180°.

∠AOC+∠BOC = 180°

∠AOC+90° = 180°

∠AOC = 180°-90°

∠AOC = 90°

We know that,the vertical angles which are created by the intersection of two straight lines,are equal.

In this case, ∠BOC and ∠AOD are vertical angles. And, ∠AOC and ∠BOD are vertical angles.

So,

∠BOC = ∠AOD

∠AOC = ∠BOD

Or,

90° = ∠AOD (By, putting the value.)

90° = ∠BOD (By, putting the value.)

Hence,the remaining angles are also 90°.