Angles of Triangles

1
Angles of Triangles

• Chapter 4, Section 2

2
Angle Sum Theorem

• The sum of angles in a triangle is 180o.

2
3
1
3
Examples

• Find the missing angles

28
82
30
?
?
?
40
68
?
4
Third Angle Theorem

• If 2 angles in one triangle are congruent to 2
  angles in a second triangle, then the third
  angles are also congruent.

58
58
62
62
60
?
5
Exterior Angle Theorem

• The measure of an exterior angle is equal to the
  sum of the two remote interior angles

The exterior angle is outside the triangle.
Also, it forms a linear pair with one angle of
the triangle.
R.I.
Exterior
R.I.
Remote interior angles are nonadjacent interior
angles.
6
Examples

• Find the measure of the exterior angle.

70
150
?
?
?
40
20
?
?
60
7
Things to think about

• The acute angles in a right triangle are always
  _______________.

complementary
30 60 90
42 48 90
53 37 90
8
Things to think about

• There can be no more than one ______________ or
  ____________ angle in a triangle.

obtuse
right
NOT TRIANGLES!!