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.

Question

asked Jun 3, 2022 143k views

1 Answer

Fiordaliza · Answer 1 · 2022-06-09T15:26:18+0000

Answer:

$\angle ABC = 122^\circ$

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:

$\angle ADC = (1)/(2) * \angle ABC$

Make ABC the subject

$\angle ABC = 2 * \angle ADC$

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

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

$\angle ABC = 122^\circ$