Question

A,B,C are three points on the circle with centre O such that angle BOC=30° and angle AOB=60° If D is a point on the circle other than the arc ABC, find angle ADC​

Answer 1

Answer:45°

Step-by-step explanation:

angle ABO = (180-60)/2=60°

angle CBO = (180-30)/2=75°

angle ABC = angle ABO + angle CBo

                  =60+75=135°

As ABCD is a cyclic quadrilateral

angle ADC + angle ABC = 180°

angle ADC = 180° - angle ABC = 180 - 135

angle ADC = 45°

Answer 2

Answer:

Given :

• A circle with centre O.

To find :

• $\angle\:\:$ ADC

Solution :

$\\ \sf \angle \: AOC = \angle \: AOB + \: \angle \: BOC \\ \\ \\ \implies \sf \: 60 {}^{ \circ} + 30 {}^{ \circ} \\ \\ \\ \implies \sf \red{90 {}^{ \circ} } \\ \\ \\ \sf \angle \: ADC = \dfrac{1}{2} \: \angle \: AOC= \dfrac{1}{2} \: (90) \\ \\ \\ \implies \sf \pink{45 {}^{ \circ} }$

( the angle subtended an arc at the centre double the angle subtended by it at the any remaining part of the circle ) .