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Question

Find the value of x in the following figure if AB || CD and BC || ED.

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Solution

Given: AB || CD and BC || DE.
ABC = 75°.

Since AB || CD, BC will be the transversal.
ABC = BCD = 75° ( Alternate interior angles) -----(i)

As BC || DE, CD will be the transversal.
BCD + CDE = 180° (Co-interior angles)
From (i), 75° + CDE = 180°.
CDE = 180° - 75° = 105°.
x = 105°.

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