Page 7 - Lesson note 5 Angle subtended by arc Ch.- 10 Circle

170⁰ = 2 BAC
0
0
BAC = 170 /2 = 85
Question 4: If O is the centre of the circle, find the value of x in each of the following
figures.

.
AOC = 135⁰ (Given)
From figure, AOC + BOC = 180⁰ [Linear pair of angles]
135⁰ + BOC = 180⁰
or BOC= 180⁰−135⁰
or BOC=45⁰
As The angle subtended by an arc at the centre is double the angle
Subtended by it at any point on the remaining part of the circle.)
BOC = 2 CPB
45⁰ = 2x
0
x = 45 /2
)
= 0

(II)

Solution:
ABC=40⁰ (given)
ACB = 90⁰ [Angle in semicircle]
In ΔABC,
CAB+ ACB+ ABC=180⁰ [angle sum property]
CAB+90⁰+40⁰=180⁰
CAB=180⁰−90⁰−40⁰
CAB=50⁰
Now, CDB = CAB [Angle is on same segment]
0
x = 50
(iii)