Question

In figure \( \angle BAP = 80^\circ \) and \( \angle ABC = 30^\circ \), then \( \angle AQC \) will be:

• A. 55°
• B. 110°
• C. 50°
• D. 65°

Hint:

In cyclic quadrilaterals, opposite angles sum up to 180°, which is useful in finding unknown angles.

Answer 1

The Correct Option is A

From the figure, we have \( \angle BAP = 80^\circ \) and \( \angle ABC = 30^\circ \). Using the property of the angle of a cyclic quadrilateral: \[ \angle AQC = 180^\circ - \angle BAP - \angle ABC = 180^\circ - 80^\circ - 30^\circ = 55^\circ \] Therefore, \( \angle AQC = 55^\circ \).