CAIE IGCSE Mathematics Extended E4.6 Angles Questions

Practise calculating and justifying angles using point, line, triangle, quadrilateral, parallel-line and regular-polygon properties.

Exam points

select the relevant point, line, triangle or quadrilateral angle sum before solving
use corresponding, alternate or co-interior facts only when the lines are established as parallel
calculate regular-polygon interior or exterior angles and use them to determine side counts

Covered syllabus points

E4.6.1 Calculate unknown angles and give simple explanations using the E4.6.2 Calculate unknown angles and give geometric explanations for angles E4.6.3 Know and use angle properties of regular and irregular polygons

[Maximum number: 10]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

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.

Figure for Question (b) — CAIE IGCSE Mathematics Extended

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

(c)

A regular pentagon has an exterior angle, d.

A regular hexagon has an interior angle, h.
Find the fraction $\frac{d}{h}$ .
Give your answer in its simplest form.

[ 4 ]

$\frac35$ cao nfww
B3 for $\frac{72}{120}$ , or B2 for d=72 or h=120, or M1 for $360\div5$ oe or $180-(360\div6)$ oe

[Maximum number: 2]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

The diagram shows two intersecting straight lines crossing two parallel lines.
Find the value of x.

[Maximum number: 2]

Find the number of sides of a regular polygon with interior angle $162^{\circ}$ .

20

M1 for $\frac{360}{180-162}$ or for $\frac{180(n-2)}{n}=162$ .

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Covered syllabus points

Question 1

Question (a)

Question (b)

Question (c)

Question 2

Question 3