Question

Find the value of x in the following figure, where O is the centre of the circle:

Answer 1

• ∠AOB = 30°
• O is the center of the circle.
• AC and BD are chords.
• x = ∠ADC, the angle subtended by chord (AC) at point (D) on the circle

Step 1: Recognize that ∠AOB is the central angle subtending the arc (AB).

Step 2: Angles subtended by the same arc in the circumference are half of the central angle.

Therefore, the angle subtended by arc (AB) at point (D), i.e., ∠ADC = `1/2 ∠AOB = 1/2  "times"  30° = 15°`

Thus, the value of x = 15