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Transcript 
• auxiliary line
• exterior angle
• remote interior angles
• flow proof
• corollary
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.
Understand
Examine the information in the diagram.
You know the measures of two angles of
one triangle and only one measure of
another. You also know that 1 and 2
are vertical angles.
Use the Triangle Angle-Sum
Theorem
Plan
Find m1 first because the measure of
two angles of the triangle are known.
Use the Vertical Angles Theorem to find
m2. Then you will have enough
information to find the measure of 3.
Solve
Triangle Angle-Sum Theorem
Simplify.
Subtract 117 from each side.
Use the Triangle Angle-Sum
Theorem
1 and 2 are congruent vertical angles. So, m2 = 63.
Triangle Angle-Sum Theorem
Simplify.
Subtract 142 from each side.
Answer: Therefore, m1 = 63, m2 = 63, and
m3 = 38.
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
Use the Exterior Angle Theorem
GARDENING Find the measure
of FLW in the fenced flower
garden shown.
mLOW + mOWL = mFLW
x + 32 = 2x – 48
Exterior Angle
Theorem
Substitution
32 = x – 48
Subtract x from
each side.
80 = x
Add 48 to each side.
Answer: So, mFLW = 2(80) – 48 or 112.
Find Angle Measures in Right Triangles
Find the measure of
each numbered angle.
Exterior Angle Theorem
m1 = 48 + 56
Simplify.
= 104
104 + m2 = 180
76
If 2 s form a linear pair, they
are supplementary.
Substitution
Subtract 104 from each side.
Find Angle Measures in Right Triangles
If 2 s form a right
angle, they are
complementary.
m 3 = 90 – 48
Simplify.
= 42
(90 – 34) + m2 + m 4 = 180
56 + 76 + m 4 = 180
132 + m4 = 180
48
Triangle Angle-Sum
Theorem
Substitution
Simplify.
Subtract 132 from each
side.
Find Angle Measures in Right Triangles
m5 + 41 + 90 = 180
m5 + 143 = 180
49
Triangle Angle-Sum Theorem
Simplify.
Subtract 131 from each side.
m1 = 104, m2 = 76, m3 = 42,
m4 = 48, m5 = 49
Find m3.
A. 50
B. 45
C. 85
D. 130
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