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