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 = 750, ∠AOC =300 then find the m∠BOC.
As ∠AOC and ∠BOC are adjacent-angles.
∴∠AOB = ∠AOC + ∠BOC
750 = 30 + ∠BOC
∴ ∠BOC = 75 - 30
∴ ∠BOC = 450
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.
___________________________________________________________________ Basic Geometry