Question

a circle is centered on point b. points a, c and d lie on its circumference. if ∠adc measures 61°, what does ∠abc measure?

Explanation:

Step1: Recall circle angle theorem

An inscribed angle is half the central angle subtending the same arc. Here, $\angle ADC$ is inscribed, $\angle ABC$ is central, both subtend arc $AC$.

Step2: Calculate central angle

Multiply inscribed angle by 2.
$\angle ABC = 2 \times \angle ADC = 2 \times 61^\circ$

Answer:

$122^\circ$