Question

A circle is centered on point B. Points A, C and D lie on its circumference.
If ZABC measures 40°, what does ZADC measure?

Answer 1

Given:

A circle is centered on point B.

Points A, C and D lie on its circumference.

If $m\angle ABC$ measures 40°.

To find:

The $m\angle ADC$.

Solution:

Central angle theorem: According to this theorem, the central angle is equal to the twice of inscribed angle on the same intercepted arc.

In the given figure $\angle ABC$ is the central angle and $m\angle ADC$ is the inscribed angle on the same arc AC.

Using central angle theorem, we get

$m\angle ABC=2m\angle ADC$

$40^\circ=2m\angle ADC$

$\dfrac{40^\circ}{2}=m\angle ADC$

$20^\circ=m\angle ADC$

Therefore, the measure of angle ADC is 20°.