Adjacent angles

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Adjacent angles :Two angles in a plane are called adjacent-angles, if

1) they have a common vertex,

2) they have a common arms (rays) , and

3) their other arms lie on the opposite sides of the common arm.


In the above figure ∠ AOC and ∠ BOC have a common vertex O. Also they have a common arm OC and their arms are OA and OB.

So ∠AOC and ∠BOC are adjacent-angles.

∠AOB = ∠AOC + ∠BOC

Examples :

1) Write down each pair of adjacent-angles from the diagram given below :


Solution :
i) ∠AOB, ∠BOC (common ray is OB and O is a common vertex)

ii) ∠AOC, ∠COD (common ray is OC and O is a common vertex)

iii) ∠BOC, ∠COD(common ray is OC and O is a common vertex)

iv) ∠AOB , ∠BOD (common ray is OB and O is a common vertex)

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2)∠AOC and ∠BOC are adjacent-angles. If m∠AOB = 750,
∠AOC =300 then find the m∠BOC.

Solution :
As ∠AOC and ∠BOC are adjacent-angles.

∴∠AOB = ∠AOC + ∠BOC

750 = 30 + ∠BOC

∴ ∠BOC = 75 - 30

∴ ∠BOC = 450

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3) The sum of two adjacent angle is 1100. If one angle is 300 more than the other. Find the measures of two angles.
Solution :
Let one angle be x.
Other angle = x + 30
Sum of two angles = 1100
∴ x + x + 30 = 110
⇒ 2x + 30 = 110
⇒ 2x = 110 - 30
⇒ 2x = 80
⇒ x = 80/2 =40
One angle = 400
So, other angle = x + 30
⇒ other angle = 40 + 30 = 700
∴ The two angles are 400 and 700.
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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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