# Adjacent angles

**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 = 75

^{0},

∠AOC =30

^{0}then find the m∠BOC.

**Solution :**

As ∠AOC and ∠BOC are adjacent-angles.

∴∠AOB = ∠AOC + ∠BOC

75

^{0}= 30 + ∠BOC

∴ ∠BOC = 75 - 30

∴ ∠BOC = 45

^{0}

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3) The sum of two adjacent angle is 110

^{0}. If one angle is 30

^{0}more than the other. Find the measures of two angles.

**Solution :**

Let one angle be x.

Other angle = x + 30

Sum of two angles = 110

^{0}

∴ x + x + 30 = 110

⇒ 2x + 30 = 110

⇒ 2x = 110 - 30

⇒ 2x = 80

⇒ x = 80/2 =40

One angle = 40

^{0}

So, other angle = x + 30

⇒ other angle = 40 + 30 = 70

^{0}

∴ The two angles are 40

^{0}and 70

^{0}.

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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

• 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