1. Lesson 4-2: Angles of Triangles
TARGETS
Apply the Triangle Angle-Sum Theorem.
Apply the Exterior Angle Theorem.
Target

2. LESSON 4-2: Angles of Triangles
Tri angle sum th

3. Use the Triangle Angle-Sum Theorem
LESSON 4-2: Angles of Triangles
EXAMPLE 1
Use the Triangle Angle-Sum Theorem
SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle.
WORK REASONS
Triangle Angle-Sum Th.
Vertical angles
1  2
m1 = m2 63 = m2
Def of Congruent
Substitution
Triangle Angle-Sum Th.
Check The sums of the measures of the angles in each triangle should be m = or 180 m2 + m = or 180
Ex1: Tri Ang Sum Th

4. LESSON 4-2: Angles of Triangles
Ex Angle The

5. Answer: So, mFLW = 2(80) – 48 or 112.
LESSON 4-2: Angles of Triangles
EXAMPLE 2
Use the Exterior Angle Theorem
GARDENING Find the measure of FLW in the fenced flower garden shown.
WORK REASONS
mLOW + mOWL = mFLW Exterior Angle Theorem
x + 32 = 2x – 48 Substitution
32 = x – 48
80 = x
Answer: So, mFLW = 2(80) – 48 or 112.
Ex2 Ext Ang Th.

6. LESSON 4-2: Angles of Triangles
EXAMPLE 3
Find Angle Measures in Right Triangles
Find the measure of each numbered angle.
WORK REASONS
Exterior Angle Theorem
m1 =
m1 = 104
Linear Pair
Substitution
104 + m2 = 180 76
m = 90
m 3 = 42
Complementary
Ex3 Right Tri

7. Find the measure of each numbered angle.
LESSON 4-2: Angles of Triangles
EXAMPLE 3
Find Angle Measures in Right Triangles
Find the measure of each numbered angle.
WORK REASONS
(90 – 34) + m2 + m 4 = 180
Triangle Sum Theorem
Substitution
m 4 = 180
132 + m4 = 180
m4 = 48
Triangle Angle-Sum Theorem
m = 180
m = 180
m5 = 49
Ex3 Right Tri