Question

In the figure, AB || DC, then the measure of ∠D is equal to

Answer 1

• In order to solve this question, we need to do some construction.
• We extend side AD to a point P .
• Now, we can see that ∠DAB and ∠PDC form a pair of corresponding angles.
• We also know that for a pair of corresponding angles, both the angles are equal to each other.
• Therefore,∠DAB = ∠PDC = 80°
• Now ∠PDC and ∠DCA form a pair of linear angles, and we know that such pair of angles are supplementary in nature.
• Therefore,

∠PDC + ∠CDA = 180°
80° + ∠CDA = 180°
∠CDA = 100°