5) Complete the proof that opposite angles of an inscribed quadrilateral are supplementary. Given: Circle C with inscribed quadrilateral DEFG Prove: mLD + mZF=180°, mZE+ m2G = 180° ww mnn By the arc addition postulate, the MEFG = 360° and mFGD , MDEF. %3D 360°. Using the Theorem, the MEDG = 2m

5) Complete the proof that opposite angles of an inscribed quadrilateral are supplementary. Given: Circle C with inscribed quadrilateral DEFG Prove: mLD + mZF=180°, mZE+ m2G = 180° ww mnn By the arc addition postulate, the MEFG = 360° and mFGD , MDEF. %3D 360°. Using the Theorem, the MEDG = 2m

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

5) Complete the proof that opposite angles of an inscribed quadrilateral are
supplementary.
Given: Circle C with inscribed quadrilateral DEFG
Prove: mLD + mLF=180°, mZE+ m2G = 180°
By the arc addition postulate, the MEFG
= 360° and mFGD , MDEF .
%3D
360°. Using the
Theorem, the
MEDG
= 2m<F, the "mEFG = 2mzD, the
%3D
MDEF
MFGD
= 2mZG, and the
Substitution Property, 2mZD +
= 2MZG, and the MFGD
= 360°, so
%3D
= 2mZE. By the
%3D
Similarly,

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