http://www.ck12.org Chapter 9. Circles
a)mF ED̂
b)mCDF̂
c)mBD̂
d)mDFĈ
Solution:Use the Arc Addition Postulate.
a)mF ED̂=mF Ê+mED̂= 120 ◦+ 38 ◦= 158 ◦
We could have labeledF ED̂asF D̂because it is less than 180◦.
b)mCDF̂=mCD̂+mDÊ+mEF̂= 90 ◦+ 38 ◦+ 120 ◦= 248 ◦
c)mBD̂=mBĈ+mCD̂= 52 ◦+ 90 ◦= 142 ◦
d)mDFĈ= 38 ◦+ 120 ◦+ 60 ◦+ 52 ◦= 270 ◦ormDFĈ= 360 ◦−mCD̂= 360 ◦− 90 ◦= 270 ◦
Example 6:Algebra ConnectionFind the value ofxfor
⊙
Cbelow.
Solution:There are 360◦in a circle. Let’s set up an equation.
mAB̂+mAD̂+mDB̂= 360 ◦
( 4 x+ 15 )◦+ 92 ◦+( 6 x+ 3 )◦= 360 ◦
10 x+ 110 ◦= 360 ◦
10 x= 250 ◦
x= 25 ◦Know What? RevisitedBecause the seats are 20◦apart, there will be^360
◦
20 ◦ =18 seats. It is important to have the
seats evenly spaced for balance. To determine how far apart the adjacent seats are, use the triangle to the right. We
will need to use sine to findxand then multiply it by 2.