Question

In the given figure, if \( \angle AOB = 125^\circ \), then \( \angle COD = \):

• A. \( 125^\circ \)
• B. \( 55^\circ \)
• C. \( 90^\circ \)
• D. \( 45^\circ \)

Hint:

The angles formed by two intersecting chords at the center of a circle are supplementary and add up to \( 180^\circ \).

Answer 1

The Correct Option is B

We are given that \( \angle AOB = 125^\circ \), and we need to find \( \angle COD \). In a circle, when two chords intersect at the center (or the angle between two radii), the angle formed by two radii is related to the angles formed at other points in the circle. We know that: \[ \angle AOB + \angle COD = 180^\circ \] This is because angles around a point add up to \( 360^\circ \), and the angles on opposite sides of the circle must be supplementary. Substitute the given angle \( \angle AOB = 125^\circ \): \[ 125^\circ + \angle COD = 180^\circ \] Solving for \( \angle COD \): \[ \angle COD = 180^\circ - 125^\circ = 55^\circ \] Thus, the correct answer is \( 55^\circ \).