Question

a circle is centered on point b. points a, c and d lie on its circumference. if ∠abc measures 40°, what does ∠adc measure? °

Explanation:

Step1: Identify angle types

$\angle ABC$ is a central angle, $\angle ADC$ is an inscribed angle subtending the same arc $\overset{\frown}{AC}$.

Step2: Apply inscribed angle theorem

The inscribed angle is half the central angle.
$\angle ADC = \frac{1}{2} \times \angle ABC$

Step3: Substitute given value

$\angle ADC = \frac{1}{2} \times 40^\circ$

Answer:

$20^\circ$