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Question
The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60°,
find the other angles.
Solution
Given AB || CD
AD || BC
Since AB || CD and AD is the transversal
`∠`A + `∠`D = 180° [Co-interior angles are supplementary]
60° + `∠`D = 180°
`∠`D = 180° - 60°
`∠`D = 120°
Now, AD || BC and AB is the transversal
`∠`A + `∠`B = 180° [Co-interior angles are supplementary]
60° + `∠`B = 180°
`∠`B = 180° - 60° = 120°
Hence `∠`A = `∠`C = 60°
ÐB = ÐD =120°
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