Angles in a triangle
Monday, 09 January 2017
Angles on a straight line Add up to 180°
B
C
C
A
A
B
C
C
B
A
A
𝑏
Angles in a triangle
add up to 180°
𝑎 + 𝑏 + 𝑐 = 180°
𝑎
𝑐
Example
Work out the size of the missing angle for each of the following
(i)
70
70 + 75 = 145
𝑎 = 180 − 145
𝑎 = 35
75
𝑎
(ii)
𝑏
63 + 43 = 107
𝑏 = 180 − 107
𝑏 = 73
63
43
(iii)
125 + 17 = 142
𝑐 = 180 − 142
17
𝑐 = 38
125
𝑐
(iv)
90 + 56 = 166
𝑑 = 180 − 166
𝑑
(v)
56
𝑑 = 14
40
180 − 40
= 140
2𝑒 = 140
𝑒 = 70
𝑒
𝑒
This triangle is known as an ISOSCELES triangle
(vi)
180 − 30 = 150
2𝑥
3𝑥 = 150
30
𝑥
𝑥
(vii)
𝑥 = 50
25 + 27 = 52
180 − 52 = 128
2𝑥 = 128
𝑥 + 27
25
𝑥 = 64
Angles in a Quadrilateral
Angles in a triangle
add up to 180°
Angles in a triangle
add up to 180°
Angles in a quadrilateral
add up to 360°
𝑐
𝑏
Angles in a quadrilateral
add up to 360°
𝑎 + 𝑏 + 𝑐 + 𝑑 = 360°
𝑎
𝑑
Example
Work out the size of the missing angle for each of the following
(i)
𝑎
94
94 + 83 + 116 = 293
𝑎 = 360 − 293
𝑎 = 67
83
116
(ii)
107
94
107 + 94 + 87 = 288
𝑏 = 360 − 288
𝑏 = 72
𝑏
87
(iii)
𝑐
134
134 + 90 + 57 = 281
𝑏 = 360 − 281
𝑏 = 79
57
(iv)
86
= 127
𝑑 = 360 − 127
𝑑
15
86 + 15 + 26
𝑑 = 233
26
(v)
𝑥
88
34 + 88 = 122
2𝑥 = 360 − 122
34
𝑥
2𝑥 = 238
𝑥 = 119
This quadrilateral is known as a KITE
Example
Two angles in a triangle are 53 and 47.
What is the size of the third angle?
53 + 47 = 100
Angle = 80°
Example
Two angles in a quadrilateral are 107 and 69. The other two angles are
equal in size.
What is the size of the other two angles?
107 + 69 = 176
360 − 176 = 184
Each Angle = 92°
Example
James measured the angles in a triangle as 46°, 78°and 55°.
Was he correct with his measurements?
4 6
7 8
+
1
5 5
1 7 9
He was not correct with his measurement.
The three angles should add up to give 180°
𝑎
𝑎
91
84
88
113
16
57
64
𝑎
65
77
48
95
101
𝑎 45
70
𝑎
62
10
68
74
54
93
𝑎
81
11
12
27
85
118
67
111
𝑎
102
86
𝑎
𝑎
𝑎
19
𝑎
33
𝑎
99
48 70 96 102
48 70 96 102
48 70 96 102
49 71 97 119
49 71 97 119
49 71 97 119
59 72 100 130
59 72 100 130
59 72 100 130
48 70 96 102
48 70 96 102
48 70 96 102
49 71 97 119
49 71 97 119
49 71 97 119
59 72 100 130
59 72 100 130
59 72 100 130
48 70 96 102
48 70 96 102
48 70 96 102
49 71 97 119
49 71 97 119
49 71 97 119
59 72 100 130
59 72 100 130
59 72 100 130
48 70 96 102
48 70 96 102
48 70 96 102
49 71 97 119
49 71 97 119
49 71 97 119
59 72 100 130
59 72 100 130
59 72 100 130
48 70 96 102
48 70 96 102
48 70 96 102
49 71 97 119
49 71 97 119
49 71 97 119
59 72 100 130
59 72 100 130
59 72 100 130
48 70 96 102
48 70 96 102
48 70 96 102
49 71 97 119
49 71 97 119
49 71 97 119
59 72 100 130
59 72 100 130
59 72 100 130
48 70 96 102
48 70 96 102
48 70 96 102
49 71 97 119
49 71 97 119
49 71 97 119
59 72 100 130
59 72 100 130
59 72 100 130
48 70 96 102
48 70 96 102
48 70 96 102
49 71 97 119
49 71 97 119
49 71 97 119
59 72 100 130
59 72 100 130
59 72 100 130
48 70 96 102
48 70 96 102
48 70 96 102
49 71 97 119
49 71 97 119
49 71 97 119
59 72 100 130
59 72 100 130
59 72 100 130
𝑎
𝑎
91
84
88
113
16
57
64
𝑎
65
77
48
95
101
𝑎 45
70
𝑎
62
10
68
74
54
93
𝑎
81
11
12
27
85
118
67
111
𝑎
102
86
𝑎
𝑎
𝑎
19
𝑎
33
𝑎
99