Question

A,B,C and D are points on the circle with centre O.AOC =100°.
Find ADC and ABC

Answer 1

Answer:

Step-by-step explanation:

We know that the angle subtended by an arc is twice the angle subtended by it on

the circumference. From the figure we know that ZAOC =

100

So we get ZAOC = 2 ZADC

It can be written as ZADC = 1/2 ZAOC

By substituting the values ZADC = 12 (100)

So we get ZADC = 50

We know that the opposite angles of a cyclic quadrilateral are supplementary

It can be written as ZADC + ZABC = 180

By substituting the values

50+ LABC = 180

On further calculation

ZABC = 180 - 50

By subtraction

ZABC = 130

Therefore, ZADC = 50 and <ABC = 130.