CK-12 Geometry - Second Edition

http://www.ck12.org Chapter 1. Basics of Geometry

Solution:From the picture, we see that the angles are congruent, so the given measures are equal.

( 5 x+ 7 )◦= ( 3 x+ 23 )◦

2 x◦= 16 ◦

x= 8 ◦

To find the measure of^6 ABC, plug inx= 8 ◦to( 5 x+ 7 )◦.

( 5 ( 8 )+ 7 )◦

( 40 + 7 )◦

47 ◦

Becausem^6 ABC=m^6 XY Z,m^6 XY Z= 47 ◦too.

Angle Bisectors

Angle Bisector:A ray that divides an angle into two congruent angles, each having a measure exactly half of the
original angle.

BDis the angle bisector of^6 ABC

(^6) ABD∼= (^6) DBC
m^6 ABD=

1

2

m^6 ABC

Angle Bisector Postulate:Every angle has exactly one angle bisector.

Example 8:Let’s take a look at Review Queue #1 again. IsOPthe angle bisector of^6 SOT? Recall, thatm^6 ROT=
165 ◦, what ism^6 SOPandm^6 POT?