If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give reason for your answer

Solution:

Given, one of the angles formed by two intersecting lines is a right angle.

We have to determine the type of the other three angles.

Consider two intersecting lines AB and CD which intersect at O.

So, ∠AOD = 90°

We know that vertically opposite angles are equal.

So, ∠AOD = ∠BOC = 90°

We know that angles on a straight line are equal to 180 degrees.

∠AOD + ∠DOB = 180°

∠DOB = 180°- 90°

∠DOB = 90°

Again vertically opposite angles, ∠DOB and ∠AOC are equal.

∠DOB = ∠AOC = 90°

Therefore, all the three angles are equal to 90 degrees.

✦ Try This: Can two right angles be complementary to each other?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

NCERT Exemplar Class 9 Maths Exercise 6.2 Problem 8

If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give reason for your answer

Summary:

If one of the angles formed by two intersecting lines is a right angle, the other three angles are also equal to 90 degrees as the angles on the straight lines equal to 180 degrees. Also, vertically opposite angles are equal

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