A circle is centered on point B, points A,C and D lie on its circumference. If angle ADC measures 62, what does angle ABC measure

Question

asked Jan 15, 2021 136k views

2 Answers

Suho · Answer 1 · 2021-01-22T08:12:56+0000

Answer:

$m\angle ABC=124^o$

Explanation:

step 1

Find the measure of arc AC

we know that

The inscribed angle is half that of the arc it comprises.

so

$m\angle ADC=(1)/(2)(arc\ AC)$

substitute the given value

$62^o=(1)/(2)(arc\ AC)$

$arc\ AC=124^o$

step 2

Find the measure of angle ABC

we know that

Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it

so

$m\angle ABC=arc\ AC$ ----> by central angle

therefore

$m\angle ABC=124^o$