AMSCO'S Geometry. New York - Rye High School

Angles Formed by Tangents, Chords, and Secants 571SolutionThe sum of the minor arc and the major arc withthe same endpoints is 360.Let x = mPQX .XThen 360 x = mPSQ.X 2 mPQ X )1mR 2 (mPSQ170 2 (360 2 x 2 x)170 2 (360 2 2x)70 180 xx 110360 x 360 110 250Answer mPQX 110 and mPSQ X 250SPQRSUMMARYType of Angle Degree Measure ExampleFormed by aTangent and aChordFormed by TwoIntersectingChordsThe measure of an angleformed by a tangent and achord that intersect at thepoint of tangency is equal toone-half the measure of theintercepted arc.The measure of an angleformed by two intersectingchords is equal to one-halfthe sum of the measures ofthe arcs intercepted by theangle and its vertical angle.A1Bm/1 5 X 12 mABDC2 1ABm/1 5 1 2 (mAB X 1 mCD X )m/2 5 1 2 (mAB X 1 mCD X )(Continued)