In the figure O is the centre of the circle. ZAOC = 80°
(a) What is the measure of ZABC ?
(b) What is the measure of ZADC ?
B.
S
80°
A
C С
D
Answers
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0
Answer:
∠ADC=50
o
and ∠ABC=130
o
Explanation:
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
o
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