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Mathematics
Mathematics
Problem
In a circle with centre
O
O
O
, points
A
A
A
and
B
B
B
lie on the circumference. The measure of
∠
A
O
B
\angle AOB
∠
A
O
B
is
(
5
x
−
20
)
∘
(5x-20)^{\circ}
(
5
x
−
20
)
∘
. At a point
C
C
C
on the circumference, the angle subtended by arc
A
B
AB
A
B
is
(
2
x
+
5
)
∘
(2x+5)^{\circ}
(
2
x
+
5
)
∘
. Calculate the value of
x
x
x
and hence find the measures of
∠
A
O
B
\angle AOB
∠
A
O
B
and
∠
A
C
B
\angle ACB
∠
A
C
B
.
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