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Question
In the given figure, O is the centre of the circle and ∠DAB = 50° . Calculate the values of xand y.
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Solution
It is given that, O is the centre of the circle and \[\angle DAB = 50° \]
We have to find the values of x and y.
ABCD is a cyclic quadrilateral and `angle A + angle C = 180°`
So,
50° + y = 180°
y = 180° − 50°
y = 130°
Clearly Δ OAB is an isosceles triangle with OA = OB and `angle OBA = angle OAB`
Then, `angle OBA + angleOAB + angle AOB = 180°`
`angleAOB = 180° - ( 50° + 50° ) ` (Since `angleOBA = angle OAB = 50°` )
So, `angleAOB = 80°`
x + `angle AOB ` = 180° (Linear pair)
Therefore, x = 180° − 80° = 100°
Hence,
x = 100° and y = 130°
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