Linear Pair Angles

Covid-19 has led the world to go through a phenomenal transition .

E-learning is the future today.

Stay Home , Stay Safe and keep learning!!!

Two adjacent angles are said to form a linear pair angles , if their non-common arms are two opposite rays.


∠BOC and ∠AOC are linear-pair-angles.

Linear-pair-angles are always supplementary.(add up to 1800)

∠BOC + ∠AOC = 1800

Examples :

1) One of the angles forming a linear-pair is a right angle. What can you say about its other angle?

Solution :
Let one of the angle forming a linear-pair be 'x' and other be y.

As ∠x = 900 is given .

We know that linear-pair-angles are supplementary.

∠x + ∠y = 1800

90 + ∠y = 180

∠y = 180 - 90

∠y = 900

If one of the angles forming a linear pair is a right angle then other angle is also right angle.

________________________________________________________________
2) ∠PQR and ∠SQR are linear-pair-angles. If ∠PQR= 4x
and ∠SQR = 2x then find the value of x and measures of each angle.

Solution :

As ∠PQR and ∠SQR form a linear-pair.

∴ ∠PQR + ∠SQR = 180

⇒ 4x + 2x = 180

⇒ 6x = 180

⇒ x = 30

m∠PQR = 4x = 4(30) = 1200

m∠SQR = 2x =2(30) = 600

________________________________________________________________
3) ∠AOC = ∠COB, then show that ∠AOC = 900

Solution :
Since ray OC stands on line AB.

∴∠AOC + ∠COB = 180 (Linear-Pair )
But ∠ AOC = ∠COB (given)
∴ ∠AOC + ∠AOC = 180
2∠AOC = 180
⇒∠AOC = 900 (Proved)

_________________________________________________________________
4) The two angles are in the ratio of 4:5. These two angles formed a linear-pair-angles. Find the measure of each.

Solution :
Let the ratio be x.

So the two angles will be 4x and 5x.

We know that linear-pair-angles are supplementary.

4x + 5x = 1800

9x = 180

x = 180 /9

x = 20

So, each angle will be ,4x = 4(20)= 800

Other angle = 5x = 5(20) = 1000
Basic Geometry

Point
Lines
Angles
Lines and Angles
Complementary angles
Supplementary angles
Vertically Opposite Angles
Linear Pair Angles
Adjacent Angles
Parallel Lines
Solved Problems on Intersecting Lines
Solved Problems on Parallel Lines

Home Page

Covid-19 has affected physical interactions between people.

Don't let it affect your learning.