Answer:
m∠ABC = 60°
m∠AOB = 120°
Step-by-step explanation:
Given: Equilateral triangle ABC is inscribed in Circle O.
In an Equilateral triangle each measures 60 degrees.
So
m∠ABC = 60°
m∠BCA = 60°
m∠CAB = 60°
Now we have to form a triangle AOB, we can form the triangle connecting the points A and B from 0.
Since it is an equilateral triangle, the line AO and BO bisect the angles ∠BAO and ∠OBA.
Therefore, each angle measures 60/2 = 30°
In the triangle AOB, the sum of the angles add upto 180 degreees.
∠AOB + ∠OBA + ∠BAO = 180
We know ∠OBA = ∠BAO = 30
Now plug in those values in above statement, we get
∠AOB + 30 + 30 = 180
∠AOB + 60 = 180
∠AOB = 180 -60
∠AOB = 120°
Therefore, answer is
m∠ABC = 60°
m∠AOB = 120°
