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Question
In a cyclic quadrilateral ABCD if AB || CD and ∠B = 70°, find the remaining angles.
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Solution
It is given that, ABCD is a cyclic quadrilateral such that AB || CD and `angle B = 70°`
Sum of pair of opposite angles of cyclic quadrilateral is 180°.
`angle B + angle D = 180°` (`angleB = 70° ` given)
So, `angle D = 110°`
Also AB || CD and BC transversal
So,
`angleB + angleC = 180°`
`angleC = 180 ° - 70° `
= 110°
Now
`angleA + angleC = 180°`
`angleA = 180 °- angleC `
= 180° - 110 °
= 70°
`angleD` = 180° - 70°
`angleD = 110°`
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