Question

The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60°,
find the other angles.

Answer 1

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°