Question

In the given figure, O is the centre of the circle. If ∠AOB = 145°, then find the value of x.

Answer 1

According to the Inscribed Angle Theorem, the angle at the circumference subtended by the same arc is half the angle at the centre subtended by the same arc. Mathematically, this is represented as:

x = `(∠AOB)/2`​

Substituting the given value:

x = `(145°)/2`​

x = 72.5°

Therefore, the value of x, the inscribed angle subtended by the arc AB, is 72.5°.