Problem preview
G-C.2 Warmup M2-030-A03-V01

Analyze relationships among inscribed angles, central angles, circumscribed angles, radii, chords, diameters, and tangents.

Find a central angle measure from its intercepted arc

Problem

Find the central angle measure when the intercepted arc is \(70^{\circ}\).

Big Picture

What this problem is really about

A central angle is recognized by its vertex at the circle’s center and its sides along radii. We’ll match those radii to the intercepted arc and use their equal degree measures, avoiding the halving rule reserved for inscribed angles.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-C.2
Category
Geometry
Domain
Circles
Objective
Analyze relationships among inscribed angles, central angles, circumscribed angles, radii, chords, diameters, and tangents.
Problem type
Find a central angle measure from its intercepted arc