linear pair angles

Linear Pair Angles

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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)

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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

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

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