Appendix A

A:07G Finding the Size of an Angle
Diagram Rule Example
b°
a° c°
triangle
a° + b° + c° = 180°
50°
70°
a°
Find the value of a.
a + 50 + 70 = 180
a + 120 = 180
∴ a = 60
b°
a°
c°
d°
quadrilateral
a° + b° + c° + d° = 360°
55°
b°
110° 115°
Find the value of b.
b + 55 + 115 + 110 = 360
b + 280 = 360
∴ b = 80
a°
b°
isosceles triangle
a° = b°
x°
3 cm
72° 3 cm
Find the value of x.
This is an isosceles
triangle since two
sides are equal.
∴ x = 72
a°
b°
c°
equilateral triangle
a° = b° = c°
y°
Find the value of y.
This is an equilateral
triangle as all sides
are equal.
∴ All angles are equal.
3y = 180
y = 60
a° b°
straight angle
a° + b° = 180°
135°
y°
Find the value of y.
135 + y = 180
∴ y = 45
a° b°
c°
angles at a point
a° + b° + c° = 360°
m°
70°
30°
40°
Find the value of m.
m + 70 + 30 + 40 = 360
m + 140 = 360
∴ m = 220
A:07H The Angle Sum of a Quadrilateral
The sum of the angles of any quadrilateral is 360° (or one revolution).
The angle sums of other polygons can be found by multiplying the number that is two less than the
number of sides by 180°:
angle sum = (n − 2) × 180°, where n is the number of sides,
eg angle sum of a hexagon = (6 − 2) × 180°
= 720°
28 NEW SIGNPOST MATHEMATICS 8