Question

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

• A. 75°
• B. 105°
• C. 135°
• D. 160°

Answer 1

The correct option is B 105°

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

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

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