The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60°. Find the other angles.
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
Therefore, 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°and∠B = ∠D = 120°