Question

In the given figure, AB is a diameter and DC || AB. If <CAB = 24°, find ∠ADC.

Answer 1

Given:

AB is diameter → ∠ACB = 90°

∠CAB = 24°

Step 1: Find ∠ABC

In triangle ABC:

24° + ∠ABC + 90° = 180°

∠ABC = 66°

Step 2: Use the parallel line condition

Since DC ∥ AB, angle ADC and angle ABC form a pair of co-interior angles on the same side of the transversal AC.

∠ADC = 180° − ∠ABC

∠ADC = 180° − 66° = 114°