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Stay Home , Stay Safe and keep learning!!! 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
1) Write down each pair of adjacent-angles from the diagram given below :
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)
2)∠AOC and ∠BOC are adjacent-angles. If m∠AOB = 75 0 ,
∠AOC =30 0 then find the m∠BOC.
As ∠AOC and ∠BOC are adjacent-angles.
∴∠AOB = ∠AOC + ∠BOC
75 0 = 30 + ∠BOC
∴ ∠BOC = 75 - 30
∴ ∠BOC = 45 0
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.
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 .
• 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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