In the diagram, point O is the center of the circle. If
m∠ABC = 70°, what is m∠AOC ?
Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
Let us suppose angle ABO = x and angle CBO = y, so,
[tex]x+y=70[/tex]
AO and BO will be same as both are radius.
Similarly, CO nd BO will be same as both are radius.
angle AOB = [tex]180-x-x=180-2x[/tex]
angle COB = [tex]180-y-y=180-2y[/tex]
Angle AOC = [tex]360-(AOB+COB)=360-(180-2x+180-2y)=360-360+2(x+y)[/tex]
Angle AOC = [tex]2(x+y)[/tex]
Putting the value of (x+y) as 70, then
[tex]Angle AOC = 2*70=140[/tex]
So te answer is 140° : Answer
Hope it will help :)