Transcript + m - geometry

Lesson 4-2: Angles of Triangles
TARGETS
• Apply the Triangle Angle-Sum Theorem.
• Apply the Exterior Angle Theorem.
LESSON 4-2: Angles of Triangles
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.
1  2
Vertical angles
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 180.
m1 + 43 + 74 = 63 + 43 + 74 or 180
m2 + m3 + 79 = 63 + 38 + 79 or 180
LESSON 4-2: Angles of Triangles
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.
LESSON 4-2: Angles of Triangles
EXAMPLE 3 Find Angle Measures in Right Triangles
Find the measure of each numbered angle.
WORK
m1 = 48 + 56
REASONS
Exterior Angle Theorem
m1 = 104
Linear Pair
104 + m2 = 180
76
m 3 + 48 = 90
m 3 = 42
Substitution
Complementary
LESSON 4-2: Angles of Triangles
EXAMPLE 3 Find Angle Measures in Right Triangles
Find the measure of each numbered angle.
WORK
(90 – 34) + m2 + m 4 = 180
56 + 76 + m 4 = 180
REASONS
Triangle Sum Theorem
Substitution
132 + m4 = 180
m4 = 48
m5 + 41 + 90 = 180
m5 + 143 = 180
m5 = 49
Triangle Angle-Sum Theorem