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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°
67°
40°
35°
35 105  40  180
33°
90  67  33  180
Triangles and Lines – Sum of the Angles in a Triangle
The sum of the angles in any triangle = 180°
105°
67°
40°
35°
35 105  40  180
33°
90  67  33  180
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°
67°
40°
35°
33°
35 105  40  180
90  67  33  180
So given a triangle, and any two angles, you could find the third angle.
missing angle  180  1  2
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 1 :
Find the missing angle in the triangle.
x
48°
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 1 :
Find the missing angle in the triangle.
missing angle  180  1  2 
x
missing angle  180  90  48
missing angle  180  138
missing angle  42
48°
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 2 :
Find the missing angle in the triangle.
15°
x
28°
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 2 :
Find the missing angle in the triangle.
missing angle  180  1  2 
missing angle  180  15  28
missing angle  180  43
missing angle  137
15°
x
28°
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 3 :
Find the missing angle in the triangle.
x
70°
150°
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 3 :
Find the missing angle in the triangle.
x
70°
?
150°
We must first find the supplementary angle for this linear pair…
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 3 :
Find the missing angle in the triangle.
x
70°
?
150°
We must first find the supplementary angle for this linear pair…
180 150  30
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 3 :
Find the missing angle in the triangle.
missing angle  180  1  2 
x
70°
missing angle  180  70  30
missing angle  180  100
missing angle  80
30°
150°
We must first find the supplementary angle for this linear pair…
180 150  30
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 4 :
Find the missing angle.
92°
x
56°
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 4 :
Find the missing angle.
missing angle  180  92  56
92°
missing angle  180  148
missing angle  32
32°
x
56°
First find the missing angle in the triangle…
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 4 :
Find the missing angle.
missing angle  180  92  56
92°
missing angle  180  148
missing angle  32
32°
x
56°
These are a linear pair so 180°- 32° = 148° …
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 4 :
Find the missing angle.
missing angle  180  92  56
92°
missing angle  180  148
missing angle  32
Do you see it ?
32°
56°
148°
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 4 :
Find the missing angle.
missing angle  180  92  56
92°
missing angle  180  148
missing angle  32
Do you see it ?
32°
148°
56°
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
missing angle  180  1  2
EXAMPLE # 5 :
Find the missing angle.
x
39°
115°
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 5 :
Find the missing angle.
x  39  115
x  154
x
39°
115°
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 6 :
Find the missing angle.
51°
85°
x
Triangles and Lines – Sum of the Angles in a Triangle
missing angle  180  1  2
EXAMPLE # 6 :
Find the missing angle.
85  51  x
34  x
51°
85°
Theorem – the measure of an
exterior angle of a triangle is
equal to the sum of the
opposite interior angles.
x
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