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G-C.2 Warmup M2-030-A06-V01

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

Find the measure of an angle formed by two chords intersecting inside a circle from the intercepted arcs

Problem

\(\text{Two}~\text{chords}\) intersect inside a circle. If the intercepted arcs measure \(80^{\circ}\) and \(40^{\circ}\), what is the angle measure?

Unworked circle diagram showing only the supplied geometric configuration and measures. Open full size
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What this problem is really about

An angle formed by chords crossing inside a circle uses the two arcs intercepted by the angle and its vertical angle. We’ll source those opposite arcs, add their measures, and take half of the sum rather than a difference.

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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 the measure of an angle formed by two chords intersecting inside a circle from the intercepted arcs