Question

Equilateral triangle ABC is inscribed in Circle O. Use the diagram to find the following measures.

please help me !!!!!

Answer 1

AB= 360/3 = 120
ABC= 180/3 = 60
AOB= 360/3 = 120

Answer 2

m∠ABC = 60°

m∠AOB = 120°

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°