if the measure of arc ABC=210°, what is the measure of angle AOC? solve and show its working
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Answer:
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
o
.
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