Warm ups
Classify ΔRST .
Find
y___
if ΔRST is an isosceles triangle with
___
RS = RT.
Find x if ΔABC is an equilateral
triangle.
4-2 ANGLES OF
TRIANGLES
Triangle Angle-Sum Theorem
Example
SOFTBALL The diagram
shows the path of the softball
in a drill developed by four
players. Find the measure of
each numbered angle.
Plan:You know that <1 and <2 are vertical angles.
Use the Ver. Angles Thm to find m<2. Then you will
have enough information to find the measure of <3.
Example
Plan
***Find m<1 first because the measure
of two angles of the triangle are known.
So, m<2 = 63.
Therefore, m<1 = 63, m<2 = 63, and m<3 = 38.
TWAP
Find the measure of 3.
A. 95
B. 75
C. 57
D. 85
Exterior Angle Theorem
Example
Find the measure of <FLW .
m<LOW + m<OWL = m<FLW Exterior Angle Thm
x + 32 = 2x – 48
32 = x – 48
80 = x
Answer: So, m<FLW = 2(80) – 48 = 112.
TWAP
The piece of quilt fabric is in the shape of a right
triangle. Find the measure of <ACD.
A. 30
B. 40
C. 50
D. 130
Corollary – statement that can be easily proved using a theorem
Example
Find the measure of
each numbered angle.
Exterior Angle Theorem
M<1 = 48 + 56
= 104
104 + m<2 = 180
76
Example continued
M< 3 = 90 – 48
= 42
Bottom angle: 90-34 = 56
56 + m<2 + m< 4 = 180
56 + 76 + m< 4 = 180
132 + m<4 = 180
48
Example cont
m<5 + 41 + 90 = 180
m<5 + 143 = 180
49
m<1 = 104, m<2 = 76, m<3 = 42,
m<4 = 48, m<5 = 49
That was a CRAZY one!!!!!!!!!!! 
TWAP
Find m<3.
A. 50
B. 45
C. 85
D. 130
Homework
• Pg. 250 #11-32 all, 46, 50