This is circle based question from Chapter name- circles

Topic – Angle properties of circles

Chapter number- 15

We have that O is the centre of the circle. If ∠AOC = 150°,we have to find

(i) ∠ABC

(ii) ∠ADC.

ICSE Avichal publication

Understanding ICSE Mathematics

Question no 2(a). Exercise 15.2

Given,

∠AOC = 150° and AD = CD

We know that an angle subtends by an arc of a circle

at the center is twice the angle subtended by the same arc

at any point on the remaining part of the circle.

(i)∠AOC = 2 × ∠ABC∠ABC = ∠AOC/2 = 150

^{o}/2 = 75^{o}(ii) From the figure, ABCD is a cyclic quadrilateral

∠ABC + ∠ADC = 180

^{o}(Sum of opposite angels in a cyclic quadrilateral

Is 180

^{o})75

^{o}+ ∠ADC = 180^{o}∠ADC + 180

^{o }– 75^{o}∠ADC = 105

^{o}