1.3. Congruent Angles and Angle Bisectors http://www.ck12.org
Example B
What is the measure of each angle?
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.
Example C
IsOPthe angle bisector of^6 SOT? Ifm^6 ROT= 165 ◦, what ism^6 SOPandm^6 POT?
Yes,OPis the angle bisector of^6 SOTaccording to the markings in the picture. Ifm^6 ROT= 165 ◦andm^6 ROS= 57 ◦,
thenm^6 SOT= 165 ◦− 57 ◦= 108 ◦. Them^6 SOPandm^6 POTare each half of 108◦or 54◦.
Watch this video for help with the Examples above.