10.4 Inscribed Angles and Polygons What is an inscribed angle? Inscribed angle: an angle whose vertex is on a circle and whose sides contain chords of the circle What is the difference between an inscribed angle and a central angle? Intercepted Arc: an arc that lies between two lines, rays, or segments Theorem: Measure of an Inscribed Angle Theorem The measure of an inscribed angle is one-half the measure of its intercepts arc. Example 1: Using Inscribed Angles Find the indicated measure a) !∠#=_________ b) measure of arc QR = _________ Example 2: Finding the Measure of an Intercepted Arc Find the measure of arc RS and !∠$#%. What do you notice about ∠$#% and ∠%&$ Theorem: Inscribed Angles of a Circle Theorem If two inscribed angles of a circle intercept the same arc, then the angles are congruent. Example 3: Finding the Measure of an Angle Given !∠' = 75 + , find !∠,.

10.4 Inscribed Angles and Polygons - WordPress.com · 6/10/2018 · Intercepted Arc: an arc that lies between two lines, rays, or segments Theorem: Measure of an Inscribed Angle

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Page 1: 10.4 Inscribed Angles and Polygons - WordPress.com · 6/10/2018 · Intercepted Arc: an arc that lies between two lines, rays, or segments Theorem: Measure of an Inscribed Angle

a) !∠#=_________

b) measureofarcQR=_________Example2:FindingtheMeasureofanInterceptedArcFindthemeasureofarcRSand!∠$#%.Whatdoyounoticeabout∠$#%and∠%&$Theorem:InscribedAnglesofaCircleTheoremIftwoinscribedanglesofacircleinterceptthesamearc,thentheanglesarecongruent.Example3:FindingtheMeasureofanAngleGiven!∠' = 75+,find!∠,.

Page 2: 10.4 Inscribed Angles and Polygons - WordPress.com · 6/10/2018 · Intercepted Arc: an arc that lies between two lines, rays, or segments Theorem: Measure of an Inscribed Angle

Tryonyourown:Determinethemeasureoftheredarcorangle.InscribedPolygons:ApolygonIsaninscribedpolygonwhenallitsverticeslieonacircle.Example4:UsingInscribedPolygonsFindthevalueofeachvariable:Tryonyourown:Findthevalueofeachvariable.Homework:3-15odd,19-21,25-30,41**

Page 3: 10.4 Inscribed Angles and Polygons - WordPress.com · 6/10/2018 · Intercepted Arc: an arc that lies between two lines, rays, or segments Theorem: Measure of an Inscribed Angle

Page 4: 10.4 Inscribed Angles and Polygons - WordPress.com · 6/10/2018 · Intercepted Arc: an arc that lies between two lines, rays, or segments Theorem: Measure of an Inscribed Angle

Page 5: 10.4 Inscribed Angles and Polygons - WordPress.com · 6/10/2018 · Intercepted Arc: an arc that lies between two lines, rays, or segments Theorem: Measure of an Inscribed Angle

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