Question

In the given figure, AD || BC. If <ACB = 30°, find DBC.

Answer 1

Given:

AD || BC (AD is parallel to BC)

∠ACB = 30°

We need to find ∠DBC.

Since AD is parallel to BC and both chords lie on the same circle, the alternate interior angles formed by the transversal AC will be equal.

Thus, ∠ACB = ∠DBC = 30°

Hence, the angle ∠DBC is 30°.

This is also supported by the geometry of the cyclic figure, where parallel chords subtend equal alternate angles at the circumference within the circle.

Therefore, the answer is 30°.

This solution corresponds to a similar problem and solution as found in the materials where AD, || BC and ∠ACB = 35°, giving ∠DBC = 35°. Here, by analogy and parallel line angle properties, for ∠ACB = 30°, ∠DBC = 30°.