What is the reason for #5?Given: Line I is an auxiliary line parallel to mProve: mz 2+mZ 4+mZ5=180°B●ED2StatementsReasons1. Line l is an auxiliary line parallel to m1. Given2. m21=m 42. Alternate Interior Angle Theorem3.3. Alternate Interior Angle Theorem4. Z DBC + m2 3 = 180°4. Linear Pair Postulate5. m Z 1+ mZ2 = Z DBC5.5.4. Substitution5. m2 2+m4+mZ5=180°5. Substitution

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Line l is an auxiliary line parallel to m

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter6: Circles

Section6.4: Some Constructions And Inequalities For The Circle

Problem 34E: A tangent ET is constructed to circle Q from external point E. Which angle and which side of...

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Question

What is the reason for #5?
Given: Line I is an auxiliary line parallel to m
Prove: mz 2+mZ 4+mZ5=180°
B
●E
D
2
Statements
Reasons
1. Line l is an auxiliary line parallel to m
1. Given
2. m21=m 4
2. Alternate Interior Angle Theorem
3.
3. Alternate Interior Angle Theorem
4. Z DBC + m2 3 = 180°
4. Linear Pair Postulate
5. m Z 1+ mZ2 = Z DBC
5.
5.
4. Substitution
5. m2 2+m4+mZ5=180°
5. Substitution

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