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

Question

asked Feb 18, 2022 114k views

1 Answer

EFeit · Answer 1 · 2022-02-22T17:50:32+0000

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

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

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

$(40^\circ)/(2)=m\angle ADC$

$20^\circ=m\angle ADC$

Therefore, the measure of angle ADC is 20°.