Inscribed Angles Inscribed Angle: its vertex is on the circle and its sides are chords. The arc that is inside the angle is known as the intercepted arc.

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Presentation transcript:

Inscribed Angles Inscribed Angle: its vertex is on the circle and its sides are chords. The arc that is inside the angle is known as the intercepted arc. Intercepted arc Inscribed Angle Measure of Inscribed Angle: A B D C The measure of the inscribed angle is ½ of the measure of its intercepted arc. mADB = ½ mAB

Inscribed Angle = ½ (intercepted arc) Using the above formula, find the inscribed angle or the intercepted arc. 90° S R Q T M N P 100° Z Y X W 115° Find mSTQ Find mZWX Find mNMP NMP = ½ (100) NMP = 50° 90 = ½ (STQ) 180° = STQ 115 = ½ (ZWX) 230° = ZWX

Theorem: If two inscribed angles of a circle intercept the same are, then the angles are congruent. Then C  D C B D E F G H C Inscribed Polygons mD + mF =180° mE + mG = 180° A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

Find the values of the variables: z y 120° 80° E F G D 80° + z = 180° z = 100° y + 120° = 180° y = 60° So… A = 80° B = 60° C = 100° D = 120° 3y + 3x = 180° 3y = 180° – 3x y = 60° – x 2y 3y 5x 3x A B C D 3y + 3x = 180° 2y + 5x = 180° 2(60 – x) + 5x = 180 120 – 2x + 5x = 180 3x = 60 x = 20 y = 60 – x y = 60 – 20 y = 40