CAIE IGCSE Mathematics Basic Angle Reasoning

Practise finding unknown angles with sums at a point, on a straight line and inside triangles or quadrilaterals, with clear reasons.

Exam points

use 360° around a point and 180° on a straight line to form the required equation
apply triangle sum 180° or quadrilateral sum 360°, including equal angles in isosceles shapes
solve labelled algebraic angles and attach the exact geometrical reason to each step

[Maximum number: 6]

(a)

The diagram shows an isosceles triangle with the base extended.
Find the value of x.

[ 3 ]

111
M2 for $180-\frac{180-42}{2}$ oe or $42+\frac{180-42}{2}$ oe, or M1 for $\frac{180-42}{2}$ oe

(b)

The diagram shows three lines meeting at a point.

The ratio a: b: c=3: 4: 5.

Find the value of c.

NOT TO SCALE

[ 3 ]

150
M1 for $\frac{k}{3+4+5}\times p$ , where p=1,3,4 or 5, or $\frac5{12}$ oe
B1 for 360 used

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