Page 154 - Math Course 3 (Book 2)

Circles: Angles and Arcs

Sum of Central Angles

Type of minor arc major arc semicircle
Arc
Definition: an arc that measures less than an arc that measures greater an arc that measures
1800. than 1800. 1800.
Example: A D JKL
E J K
AC DFE
1100 600
C
B G N
M L
F
JML
Named: usually by the letters of the two by the letters of the endpoints by the letters of the two
endpoints. and two endpoints and another endpoints and another
point on the arc. point on the arc.
AC
DFE mJML and JKL
Arc Degree the measure of the central 360 minus the measure of the 360 ÷ 2 or 180
Measure angle. minor arc with the same
Equals endpoints mJML = 180
m∠ABC = 110,
mDFE = 360 – mDE mJKL = 180
so mAC = 110
mDFE = 360 – 60
or 300

Let’s Begin

Measures of Central Angles

Example

The sum of the measure of ∠RTS, ∠STU, and ∠UTV
is 180.
ALGEBRA
RV is a diameter of ⊙T. Find m∠RTS. m∠RTS + m∠STU + m∠UTV = 180

R (8x – 4) + (13x – 3) + (5x + 5) = 180 Substitution
Q S 26x – 2 = 180 Simplify.

(8x – 4)0 26x = 182 Add 2 to each side.
T Divide each side
x = 7
by 26.
(13x – 3)0
20x0 Use the value of x to find m∠RTS.
m∠RTS = 8x – 4 Given
= 8(7) – 4 or 52 Substitution
(5x + 5)0 U

Answer 52
V
146