triangles and lines – sum of the angles in a triangle the sum of the angles in any triangle =...

Triangles and Lines – Sum of the Angles in a Triangle

The sum of the angles in any triangle = 180°

Triangles and Lines – Sum of the Angles in a Triangle

The sum of the angles in any triangle = 180°

105°40°

35°33°

67°

1804010535 180336790

Triangles and Lines – Sum of the Angles in a Triangle

The sum of the angles in any triangle = 180°

105°40°

35°33°

67°

1804010535 180336790

So given a triangle, and any two angles, you could find the third angle.

Triangles and Lines – Sum of the Angles in a Triangle

The sum of the angles in any triangle = 180°

105°40°

35°33°

67°

1804010535 180336790

So given a triangle, and any two angles, you could find the third angle.

21180 angle missing

Triangles and Lines – Sum of the Angles in a Triangle

48°

x

21180 angle missing

EXAMPLE # 1 : Find the missing angle in the triangle.

Triangles and Lines – Sum of the Angles in a Triangle

48°

x

21180 angle missing

EXAMPLE # 1 : Find the missing angle in the triangle.

42 angle missing

138180 angle missing

4890180 angle missing

21180 angle missing

Triangles and Lines – Sum of the Angles in a Triangle

15°

x

21180 angle missing

EXAMPLE # 2 : Find the missing angle in the triangle.

28°

Triangles and Lines – Sum of the Angles in a Triangle

15°

x

21180 angle missing

EXAMPLE # 2 : Find the missing angle in the triangle.

28°

137 angle missing

43180 angle missing

2815180 angle missing

21180 angle missing

Triangles and Lines – Sum of the Angles in a Triangle

150°

x

21180 angle missing

EXAMPLE # 3 : Find the missing angle in the triangle.

70°

Triangles and Lines – Sum of the Angles in a Triangle

150°

x

21180 angle missing

EXAMPLE # 3 : Find the missing angle in the triangle.

70°

We must first find the supplementary angle for this linear pair…

?

Triangles and Lines – Sum of the Angles in a Triangle

150°

x

21180 angle missing

EXAMPLE # 3 : Find the missing angle in the triangle.

70°

We must first find the supplementary angle for this linear pair…

?

30150180

Triangles and Lines – Sum of the Angles in a Triangle

150°

x

21180 angle missing

EXAMPLE # 3 : Find the missing angle in the triangle.

70°

We must first find the supplementary angle for this linear pair…

30°

30150180

80 angle missing

100180 angle missing

3070180 angle missing

21180 angle missing

Triangles and Lines – Sum of the Angles in a Triangle

x

92°

21180 angle missing

EXAMPLE # 4 : Find the missing angle.

56°

Triangles and Lines – Sum of the Angles in a Triangle

x

92°

21180 angle missing

EXAMPLE # 4 : Find the missing angle.

56°

32 angle missing

148180 angle missing

5692180 angle missing

32°

First find the missing angle in the triangle…

Triangles and Lines – Sum of the Angles in a Triangle

x

92°

21180 angle missing

EXAMPLE # 4 : Find the missing angle.

56°

32 angle missing

148180 angle missing

5692180 angle missing

32°

These are a linear pair so 180°- 32° = 148° …

Triangles and Lines – Sum of the Angles in a Triangle

148°

92°

21180 angle missing

EXAMPLE # 4 : Find the missing angle.

56°

32 angle missing

148180 angle missing

5692180 angle missing

32°

Do you see it ?

Triangles and Lines – Sum of the Angles in a Triangle

148°

92°

21180 angle missing

EXAMPLE # 4 : Find the missing angle.

56°

32 angle missing

148180 angle missing

5692180 angle missing

32°

Do you see it ?

Theorem – the measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.

Triangles and Lines – Sum of the Angles in a Triangle

x

39°

21180 angle missing

EXAMPLE # 5 : Find the missing angle.

115°

Triangles and Lines – Sum of the Angles in a Triangle

x

39°

21180 angle missing

EXAMPLE # 5 : Find the missing angle.

115°

154

11539

x

x

Triangles and Lines – Sum of the Angles in a Triangle

x85°

21180 angle missing

EXAMPLE # 6 : Find the missing angle.

51°

Triangles and Lines – Sum of the Angles in a Triangle

x85°

21180 angle missing

EXAMPLE # 6 : Find the missing angle.

51°

x

x

34

5185

Theorem – the measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.