Points A, B, and C lie on a circle centered at O. If angle AOC = 100 degrees, what is the measure of the inscribed angle ABC subtending the major arc AC?
Answer and explanation
Correct answer: C. 130 degrees
- Step 1: Central angle subtending the minor arc AC is 100 degrees.
- Step 2: The central angle subtending the major arc AC is 360 - 100 = 260 degrees.
- Step 3: An inscribed angle intercepting the major arc has measure equal to half of this central angle: angle ABC = 260 / 2 = 130 degrees.
- Step 4: (Alternatively, the inscribed angle intercepting the minor arc is 100 / 2 = 50 degrees, and opposite angles in a cyclic quadrilateral sum to 180 degrees: 180 - 50 = 130 degrees).
Answer
130 degrees.
Why not the others: 50 degrees is the inscribed angle subtending the minor arc; 100 degrees is the central angle; 80 degrees is 180 - 100.
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