Question

A circle is centered on point b . Points a,c, and d lie on its circumference . If adc measure 61 then what does abc measure.

Answer 1

Answer:

$\angle ABC = 122^\circ$

Step-by-step explanation:

Given

$\angle ADC = 61^\circ$

See attachment for circle

Required

Find $\angle ABC$

From the attachment, we can see that:

$\angle ADC$ is at the circumference

$\angle ABC$ is in at the center

From cyclic theorems,

The relationship between ABC and ADC is:

$\angle ADC = \frac{1}{2} * \angle ABC$

Make ABC the subject

$\angle ABC = 2 * \angle ADC$

Substitute: $\angle ADC = 61^\circ$

$\angle ABC = 2 * 61^\circ$

$\angle ABC = 122^\circ$