Interior and Exterior Angles of Triangles

Right Angle

A right angle has a measurement of 90 degrees90

Straight Angle

180A straight angleHas a measurementOf 180 degrees

Acute Angle

An acute angle hasA measurement ofLess than 90 degrees

Obtuse Angle

An obtuse angle hasA measurement ofMore than 90 degrees

Complimentary Angles

• Their measures add up to exactly 90 degrees

60

30

Supplementary Angles

• Their measures add up to exactly 180 degrees

60120

Finding Missing Angles

25º

x

x + 25 = 90

45º xx + 45 = 180

Finding the complimentary and supplementary angles

30° Complimentary: 30 + x = 90Supplementary: 30 + x = 180

The complimentary angle is 60⁰ and the supplementary angle is 150⁰

65°

The complimentary angle is ___⁰ and the supplementary angle is _____⁰

105°

In this case there is no complimentary angle, only a supplementary angle. Why?

Triangles

Finding a Missing Angle

• The sum of all angles in a triangle is 180 degrees.

• You should remember that from last year, but why?

Let’s Look at it Three Ways

• Cutting off the angles

1

2

31

2

3

I cut off angles 2 and 3 and lined them up to form a straight line

Rotating the Triangle

1

2

3

1

2

3

3 1

2

In this picture angles 1, 2, and 3 combine to make a straight line of 180⁰

Using parallel lines and transversals

1

2

3

2 31

Angle 2 by vertical angles, angles 1 and 3 by complimentary angles

Putting it into action

85

60

x

180 60 85 x 180 145 x

35 x

Your Turn

60 65

x

Finding an exterior angle-Create a straight line to solve

45 80

55

x

180 80 x

100x

80⁰ + x⁰ make up the straight line. The 55⁰ and 45⁰ have nothing to do with it.

Your Turn

x

35°

55°

60º

60º

60º x

145ºx

y

Find all the missing angles

85° 154°

Closure

• Two angles that are supplementary add up to ______

Closure

• Two angles that are complimentary add up to ______

Closure

• A straight line is _______

Closure

• The sum of all angles in a triangle equals:

Closure: With a partner find all the missing angles

125° 168°