Answered: In circle of center O, CA, AB and CD…

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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In circle of center O, CA, AB and CD are secant. If α=80° and β=50°, then angle "x" measures?

Expert Solution

Step 1: find angle ACB

Vertical angles are formed when two lines meet each other at a point.. They are always equal to each other.

For the given figure

$m angle C A B equals alpha equals 80 degree space left parenthesis space v e r t i c a l space a n g l e s space right parenthesis a n d space m angle C B A equals beta equals 50 degree space left parenthesis space v e r t i c a l space a n g l e s space right parenthesis i n space triangle A B C m angle C A B plus m angle C B A plus m angle A C B equals 180 80 plus 50 plus m angle A C B equals 180 m angle A C B equals 180 minus 130 m angle A C B equals 50$