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# Linear Pair Angles

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 = 180
0

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 = 90
0 is given .

We know that linear-pair-angles are supplementary.

∠x + ∠y = 180
0

90 + ∠y = 180

∠y = 180 - 90

∠y = 90
0

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

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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) = 120
0

m∠SQR = 2x =2(30) = 60
0

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3) ∠AOC = ∠COB, then show that ∠AOC = 90
0

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 = 180
0

9x = 180

x = 180 /9

x = 20

So, each angle will be ,4x = 4(20)= 80
0

Other angle = 5x = 5(20) = 100
0
Basic Geometry

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

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