The measure of the angle ∠AOC or m⏜AC if the measure of the ∠ABC is 75° is 150°.
What is the relation between Angles at center and circumference?
The angle made by an arc at any point on the circle (Circumference) is half the angle made by the arc at the center of the circle.
We know that the angle made by an arc of the circle at any point on the circle is half the angle made by that arc at the center of the circle. And as the measure of the ∠ABC is given, therefore, the angle made by the arc AC at the center of the circle will be twice the ∠ABC.
[tex]\angle AOC = 2 \times \angle ABC\\\\\angle AOC = 2 \times 75^o\\\\\angle AOC = 150^o[/tex]
Hence, the measure of the angle ∠AOC or m⏜AC is 150°.
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