SAT Math: Inscribed Angle Theorem (Angle Subtended by Same Arc is Half Central Angle)
By the Inscribed Angle Theorem, an inscribed angle is half the central angle intercepting the same arc: 70 / 2 = 35 degrees.
Exact Question Text
In a circle with center O, central angle AOC measures 70 degrees. Point B lies on the circle such that angle ABC intercepts arc AC. What is the measure of angle ABC?
1. Step-by-Step Formal Solution
- Inscribed angle = 1/2 * Central angle.
- Angle ABC = 70 / 2 = 35 degrees.
2. Fast Desmos / Calculator Shortcut
Evaluate 70 / 2 = 35.
3. Distractor Trap Analysis
- Trap A (Sign Flip): Forgetting to reverse inequality or dropping negative sign.
- Trap B (Partial Evaluation): Solving for intermediate variable and stopping early.
- Trap C (Extreme Assumption): Over-inferring beyond textual evidence.
- Option Correct: Accurately satisfies all algebraic and logical constraints.
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