Question

a circle is centered on point B. Points a, c and d lie on its circumference.

if angle ADC measures 23°, what does angle ABC measure?

Answer 1

Answer:

$m\angle ABC=46^o$

Step-by-step explanation:

step 1

we know that

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

so

$m\angle ADC=\frac{1}{2}(arc\ AC)$

we have

$m\angle ADC=23^o$

so

$23^o=\frac{1}{2}(arc\ AC)\\arc\ AC=46^o$

step 2

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

$m\angle ABC=46^o$