Angles of Triangles

Chapter 4, Section 2

Angle Sum Theorem

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

1

2

3

1 2 3 180m m m

Examples:

• Find the missing angles:

?

30

40

28 82

68

?

?

?

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.

62 62

58 58

60 ?

Exterior Angle Theorem

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

R.I.

R.I.

Exterior

The exterior angle is outside the triangle. Also, it forms a linear pair with one angle

of the triangle.

Remote interior angles are nonadjacent interior angles.

Examples

150

Find the measure of the exterior angle.

?

60

2040

70

?? ?

?

Things to think about:

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

42

3037

42 + 48 = 90 30 + 60 = 90 53 + 37 = 90

complementary

Things to think about:

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

right obtuse

NOT TRIANGLES!!