Page 14 - Cambridge IGCSE Mathematics Core and Extended

Example 7
Find the value of x in the triangle
on the right. 80°
41° x
Solution
x + 41° + 80° = 180° The sum of the angles of a triangle is 180°.
x = 180° – 41° – 80°
= 59°
F. Exterior angle of a triangle

An exterior angle of a triangle is the angle formed when one side
of a triangle is extended. Exterior angle

The exterior angle is equal to the sum of the two opposite interior angles.
For example,
a
c = a + b
b c

Example 8
Find the values of x and y. 80°
y
x
Solution
In the isosceles triangle, the base angles are equal.
x + x + 80° = 180°
2x + 80° = 180°
2x = 180° – 80°
2x = 100°
x = 50°
y = 80° + x Exterior angle = Sum of the
y = 80° + 50° opposite interior angles.
= 130°
G. Problem-solving

Example 9
P T
In the diagram, PR and ST are straight x 67°
lines. Find the value of x. Q
40°
Solution S
20°
In ∆ QRT, R
/TQR + 67° + 20° = 180°
/TQR = 180° – 67° – 20°
= 93°

/PQS = /TQR = 93° Vertically opposite angles
In ∆ PQS,
x + 40° + 93° = 180°
x = 180° – 40° – 93°
= 47°

154 Cambridge IGCSE Mathematics

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