Problem preview
G-C.2 Warmup M2-030-A01-V01

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

Find an inscribed angle measure from its intercepted arc

Problem

Find the inscribed angle measure when the intercepted arc is \(80^{\circ}\).

Big Picture

What this problem is really about

Before using an arc-angle rule, we need to identify where the angle’s vertex lies and which arc its sides intercept. We’ll confirm the angle is inscribed, match it to the opposite arc endpoints, and apply the one-half relationship.

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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 an inscribed angle measure from its intercepted arc