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

`m\angle ABC=46^o`

Explanation:

step 1

we know that

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

so

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

we have

`m\angle ADC=23^o`

so

`23^o=(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`