Question

A
D
2) In the figure, ZABC = 100°, then
the mZADC is
B
C С
a)
500
b) 80°
c) 100°​

Answer 1

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

∠AOC=100

o

So we get

∠AOC=2∠ADC

It can be written as

∠ADC=

2

1

(100

o

)

So we get

∠ADC=50

o

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

It can be written as

∠ADC+∠ABC=180

o

By substituting the values 50

o

+∠ABC=180

o

On further calculation

∠ABC=180

o

−50

o

By subtraction

∠ABC=130

o

Therefore, ∠ADC=50

o

and ∠ABC=130°