8th Grade
Math
LESSON 3.2
ANGLES OF TRIANGLES
The angles inside a polygon are called
interior angles. When the sides of a polygon
are extended, other angles are formed. The
angles outside the polygon that are adjacent
to the interior angles are called exterior
angles.
DEFINITION
The sum of the interior
angle measures of a
triangle is 180º
Key Idea
Interior angle measure
of a triangle
xº
yº
zº
xº
yº
zº
yº
zº
xº
xº
zº
yº
x°
32°
x + 32 + 48 = 180
x + 80 = 180
x = 100
48°
(x+28)°
x°
x+(x+28)+90 = 180
2x+118 = 180
2x = 62
x = 31
81 + 25 + x = 180
81°
x°
106 + x = 180
25°
x = 74
x°
(x-35)°
43°
x + (x-35) + 43 = 180
2x + 8 = 180
2x = 171
x = 86
The measure of an exterior
angle of a triangle is equal to
the sum of the measures of the
two nonadjacent interior angles.
Key Idea
Exterior angle measure
of a triangle
xº
yº
zº
xº
yº
zº
zº
yº
xº
zº
xº
yº
x°
36°
72°
36 + 72 = x
108 = x
2a = (a - 5) + 80
2a = a + 75
a = 75
80°
(a - 5)°
2a°
55 + 50 = x
105 = x
55°
x°
50°
32 + 90 = x
122 = x
x°
32°