Question

In the diagram below, the measure of angle XAY is 72° (m∠XAY = 72°). Since the measure of the intercepted arc XY is 144°, a student named Naomi mistakenly claims that the measure of ∠XBY is also 144°.

a. In a short paragraph, explain the source of Naomi’s error. In your response, be sure to describe the problem in terms of the following two formulas:

inscribed angle = 1/2 · (intercepted arc) and
intercepted arc = central angle.

Be sure to use important vocabulary like “inscribed angle,” “central angle”, and “intercepted arc”.

Answer 1

Angle of the intercepted arc is equal to the angle at the centre (central angle) but B is not the centre hence XBY is not 144°.

Angle at the circumference (inscribed angle) is half of the central angle, but XBY is not the central angle, so it's not 2×72.

Hence not 144°