Transcript Angles Inside the Triangle 4-1A

4-2 Angles of Triangles
You classified triangles by their side or angle
measures.
• Apply the Triangle Angle-Sum Theorem.
• Apply the Exterior Angle Theorem.
The Three Angles
1. Number the angles of your triangle.
• Fold the top angle (1) to touch the
opposite side.
• Fold the side angles (2 & 3) to meet
angle 1.
1. What do you notice?
Triangle Angle-Sum Theorem
The sum of the measures of the
angles of a triangle is 180°
Page 246
Try It
Two angles of a triangle measure
40° and 58°. What is the measure
of the third angle?
82°
?
58°
40°
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.
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.
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
Find the measure of 3.
A. 95
B. 75
C. 57
D. 85
Exterior Angle
An exterior angle is formed by
extending one of the side of the
triangle.
Exterior angle
Adjacent Interior Angle…
The interior angle in a linear pair
with an exterior angle.
An exterior angle
Adjacent interior angle
Remote Interior Angles
The two angles that are away from
the exterior angle.
Remote interior angle
Exterior angle
Remote interior angle
GARDENING Find the
measure of FLW in the
fenced flower garden shown.
mLOW + mOWL = mFLW Exterior Angle
Theorem
x + 32 = 2x – 48
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 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.
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.
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
• What is a triangle?
A figure formed by three line segments that
connect three noncollinear points.
• What is the sum of the measures of the
interior of any triangle?
The sum of the measures of the angles of a
triangle is 180°
• How are triangles classified and named?
Triangles are classified by sides and angles.
Sides: scalene, isosceles and equilateral.
Angles: acute, obtuse, right and equiangular.
4-2 Assignment
Page 250, 12 – 27
Skip 16
Show how you got
your answer
(180 - ? - ? = answer)