The measure of angle OAC is 55⁰
The angle of the major arc was given as 220⁰.
360⁰-220⁰ = 140⁰
The supplementary angle is 180⁰. Sides OA and OB are equal. Then the base angles also have to be equal.
2x + 140⁰ = 180⁰
x = 20⁰
Using the circle theorem, angle at C = 220/2 given that angle at center is 2 times angle at the circumference.
= 110⁰
2y + 110⁰ = 180⁰
y = 35⁰
angle OAC = x + y
= 20⁰ + 35⁰
= 55⁰
What is the circle theorem?
This is a part of geometry that has to do with the tangent, area, sectors or angle of a circle.
Read more on circle theorem here:
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