Given:
In circle D, the measure of angle ADC is 108 degrees.
To find:
The measure of angle ABC.
Solution:
Central angle theorem: According to this theorem, the measure of central angle of an arc is twice of the measure of inscribed angle on that arc.
Using the Central angle theorem, we get
[tex]m\angle ADC=2\times m\angle ABC[/tex]
[tex]108^\circ=2\times m\angle ABC[/tex]
[tex]\dfrac{108^\circ}{2}= m\angle ABC[/tex]
[tex]54^\circ= m\angle ABC[/tex]
Therefore, the measure of angle ABC is 54 degrees.
