10.4 Inscribed Angles and Polygons

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10.4 Inscribed Angles and Polygons

What We will Learn Use inscribed angles Use inscribed polygons

Needed Vocab Inscribed angle: angle whose vertex is on a circle and whose sides contain chords Intercepted arc: arc that lies between two lines, rays, or segments Inscribed polygon: when all vertices lie on a circle Circumscribed circle: circle that contains the vertices of the polygon

Ex. 1 Using Inscribed Angles Measure of an inscribed angle is one-half the measure of its intercepted arc Find the indicated measure A. 𝑚∠𝑇 24° B. arc QR 80°

Ex. 2 Finding Measure of Intercepted Arc Find arc RS and 𝑚∠𝑆𝑇𝑅. Arc RS 62° 𝑚∠𝑆𝑇𝑅 31°

Ex. 3 Finding Angle Measure Given 𝑚∠𝐸=75°, find 𝑚∠𝐹. 75°

Ex. 4 Using Inscribed Polygons Find each value 2𝑥=90 2𝑥 2 = 90 2 𝑥=45° B. find y and z degrees Remember that opposite angles of an inscribe polygon are supplementary. Y: 60 Z: 100