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Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180°

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Page 1: 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°

Page 2: 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

Page 3: 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

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

Page 4: 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

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

21180 angle missing

Page 5: 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

48°

x

21180 angle missing

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

Page 6: 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

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

Page 7: 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

15°

x

21180 angle missing

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

28°

Page 8: 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

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

Page 9: 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

150°

x

21180 angle missing

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

70°

Page 10: 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

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…

?

Page 11: 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

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

Page 12: 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

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

Page 13: 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

x

92°

21180 angle missing

EXAMPLE # 4 : Find the missing angle.

56°

Page 14: 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

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…

Page 15: 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

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° …

Page 16: 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

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 ?

Page 17: 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

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.

Page 18: 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

x

39°

21180 angle missing

EXAMPLE # 5 : Find the missing angle.

115°

Page 19: 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

x

39°

21180 angle missing

EXAMPLE # 5 : Find the missing angle.

115°

154

11539

x

x

Page 20: 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

x85°

21180 angle missing

EXAMPLE # 6 : Find the missing angle.

51°

Page 21: 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

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.