Answer:
[tex]\angle ABC = 122^\circ[/tex]
Step-by-step explanation:
Given
[tex]\angle ADC = 61^\circ[/tex]
See attachment for circle
Required
Find [tex]\angle ABC[/tex]
From the attachment, we can see that:
[tex]\angle ADC[/tex] is at the circumference
[tex]\angle ABC\\[/tex] is in at the center
From cyclic theorems,
The relationship between ABC and ADC is:
[tex]\angle ADC = \frac{1}{2} * \angle ABC[/tex]
Make ABC the subject
[tex]\angle ABC = 2 * \angle ADC[/tex]
Substitute: [tex]\angle ADC = 61^\circ[/tex]
[tex]\angle ABC = 2 * 61^\circ[/tex]
[tex]\angle ABC = 122^\circ[/tex]
