Question

In the accompanying diagram, AB || DE, BL BE, and AC L BD.
If A=35, find the measure of D.

Answer 1

∠ D = 55°

Explanation:

given AC is perpendicular to BD , then ∠ ACB = 90°

the sum of the 3 angles in Δ ABC is 180° , that is

∠ A + ∠ ABC + ∠ ACB = 180°

35° + ∠ ABC + 90° = 180°

125° + ∠ ABC = 180° ( subtract 125° from both sides )

∠ ABC = 55°

given AB and DE are parallel , then

∠ D and ∠ ABC are alternate angles and are congruent , so

∠ D = 55°