9.4. Inscribed Angles http://www.ck12.org
Solution:To findx, use 4 ACE.m^6 ACE= 14 ◦because it is half ofmBÊby the Inscribed Angle Theorem.
32 ◦+ 14 ◦+x◦= 180 ◦
x= 134 ◦To findy, we will use 4 EF D.
m^6 F ED= 180 ◦−x◦
m^6 F ED= 180 ◦− 134 ◦= 46 ◦m^6 BDE=m^6 ACE= 14 ◦because they intercept the same arc, Theorem 9-8. Let’s solve foryin 4 EF D, using the
Triangle Sum Theorem.
46 ◦+ 14 ◦+y◦= 180 ◦
y= 120 ◦Know What? RevisitedYou can take the picture from anywhere on the semicircular walking path. The best place
to take the picture is subjective, but most would think the pale green frame, straight-on, would be the best view.
Review Questions
QuadrilateralABCDis inscribed in
⊙
E. Find: