SAT Circles Practice Question 11 (Medium)

Math · Geometry and TrigonometryMedium

Points $A$ , $B$ , and $C$ lie on a circle. Inscribed angle $ABC$ intercepts arc $AC$ , which measures $110^\circ$ . What is the measure of angle $ABC$ ?

$55^\circ$

$35^\circ$

$110^\circ$

$220^\circ$

Show answer and explanation

Answer: A

The measure of an inscribed angle is half the measure of its intercepted arc. So angle $ABC$ measures $\frac{110^\circ}{2} = 55^\circ$ .

Choice C treats the inscribed angle like a central angle, whose measure equals its intercepted arc.

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