key
Advanced Geometry
8.3: Arcs and Central Angles Homework
Name:____________________
1. What is the difference between a major and minor arc? Explain using the picture and a few sentences.
A
E
D
C
Given circle A, find the measures of the arcs. Are the arcs congruent?
2.
! and mEF
!
mBC
3.
! and mDE
!
mCD
4.
" and mDEF
"
mBCD
5.
" and mCBF
"
mBFE
maajer@umaigortheamIethajginselessthanlsoandisThemajorarcisgreokrthan18OandisADTinthepictue.oMBC-58mCD-72mEF-58cmDEns78CongnentcongnentmBCD-130mBFF-l58mDEI-13oomCBIl58CongnentCongruent44B60BCi44J136J44o44D369jIY5oJ13DIo.T
Find the measure of each arc.
6.
mBA
m∠BOA = 44°
7.
A
B
mBC
O
C
8.
mCD
9.
mACB
10.
D
mBCD
11.
mAD
Find the indicated arc length
A
12. Arc length of AB
'T
r3TED
13. Arc length of BDA
6 cm
o
B
o?sIi¥#
90
D
For 14 – 16: Lucy had to buy a new wheel for her bike. The bike wheel has a diameter of 20 inches.
14. If Lucy rolls the wheel one complete rotation along the ground, how far will the wheel travel?
Round your answer to the nearest hundredth of an inch.
ad
C-
=
H2o)=
62.83€
15. If the bike wheel is rolled along the ground so that it rotates 45°, how far will the wheel travel?
Round your answer to the nearest hundredth of an inch.
4¥o÷lx)=
7.85€
16. If the bike wheel is rolled along the ground for 10 inches, through what angle does the wheel
rotate? Round your answer to the nearest tenth of a degree.
lo=¥o
¥=
205*36X=57€
3¥17
.H2d
oo
Use the figure at the right to answer 17, 18, and 19.
E
17. Find the value of x.
6×+5
+5×+3+8×+1=180
(5x + 3)o
iaxtao
,EQfn→x#
18. Find the mDE
(8x + 1)o
(6x + 5)o
A
Q
5191+3
48€
B
19. Find the length of AE.
mAFE6gayt5
D
Feet
.tt
6.2€
)
6 cm
C