Inscribed angles [11.3] Objectives Students will be able to… Find the measure of an inscribed angle Find the measures of an angle formed by a tangent and.

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Presentation transcript:

Inscribed angles [11.3] Objectives Students will be able to… Find the measure of an inscribed angle Find the measures of an angle formed by a tangent and a chord

Inscribed Angle Theorem Inscribed Angle : sides are chords, vertex is on the circle THEOREM : The measure of an inscribed angle is half the measurement of the intercepted arc

Example #1 Find the value of each variable.

Corollaries to Inscribed Angle Theorem 1.) 2 inscribed angles that intercept the same arc are congruent 2.) An angle inscribed in a semicircle is a right angle 3.) The opposite angles of a quadrilateral inscribed in a circle are supplementary.

Example #2 Find the values of the variables

Example #3 and #4 Find the value of the variables.

Theorem The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc

Example #5: Find x.

Example #6: Find the value of a.