Question on: WAEC Mathematics - 2010
In the diagram, 0 is the centre of the circle. Find the value x
A
34
B
29
C
17
D
14
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Correct Option: D
POQ in a straight line
Hence, < POQ + < QOR = 180o
56o + < QOR = 180o
< QOR = 180o - 56o
= 124o
Now, in \(\bigtriangleup\) QOR OR = OQ = Radius
< ORQ = < OQR = 2x (Base angles of an Isosceles \(\bigtriangleup\))
2x + 124 + 2x = 180o
4x + 124 = 180
4x = 180 - 124
4x = 56
x = \(\frac{56}{4}\)
x = 14o
Hence, < POQ + < QOR = 180o
56o + < QOR = 180o
< QOR = 180o - 56o
= 124o
Now, in \(\bigtriangleup\) QOR OR = OQ = Radius
< ORQ = < OQR = 2x (Base angles of an Isosceles \(\bigtriangleup\))
2x + 124 + 2x = 180o
4x + 124 = 180
4x = 180 - 124
4x = 56
x = \(\frac{56}{4}\)
x = 14o
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