Cambridge IGCSE Maths: Geometry — Practice Questions & Answers
Geometry on IGCSE 0580 rewards precise vocabulary and a small set of reliable angle and shape rules. This guide covers geometrical terms, angle facts on lines, at a point and across parallel lines, angle sums for triangles and polygons, the circle theorems, congruence and similarity with length, area and volume scale factors, symmetry, ruler-and-compass constructions, nets, and bearings.
122 practice questions available for this topic — here are 10 with full answers and explanations.
What is the name of a polygon with exactly $6$ sides?
Hexagon
Pentagon
Octagon
Heptagon
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WhyA polygon with $6$ sides is a hexagon; a pentagon has $5$ and an octagon has $8$.
2Multiple choice · Easy
Two angles lie on a straight line. One angle is $115^{\circ}$. What is the other angle?
$65^{\circ}$
$75^{\circ}$
$245^{\circ}$
$115^{\circ}$
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WhyAngles on a straight line add up to $180^{\circ}$, so the other angle is $180^{\circ}-115^{\circ}=65^{\circ}$.
3Multiple choice · Easy
Three angles meet at a point. Two of them are $130^{\circ}$ and $90^{\circ}$. What is the third angle?
$140^{\circ}$
$40^{\circ}$
$220^{\circ}$
$130^{\circ}$
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WhyAngles at a point add up to $360^{\circ}$, so the third angle is $360^{\circ}-130^{\circ}-90^{\circ}=140^{\circ}$.
4Multiple choice · Easy
In a triangle, two of the angles are $50^{\circ}$ and $60^{\circ}$. What is the third angle?
$70^{\circ}$
$110^{\circ}$
$80^{\circ}$
$60^{\circ}$
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WhyAngles in a triangle add up to $180^{\circ}$, so the third angle is $180^{\circ}-50^{\circ}-60^{\circ}=70^{\circ}$.
5Multiple choice · Easy
How many lines of symmetry does a square have?
$4$
$2$
$1$
$8$
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WhyA square has $4$ lines of symmetry: two through opposite sides and two through opposite corners.
6Multiple choice · Easy
What is the order of rotational symmetry of an equilateral triangle?
$3$
$1$
$6$
$2$
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WhyAn equilateral triangle maps onto itself $3$ times in a full turn, so its order of rotational symmetry is $3$.
7Multiple choice · Easy
Two parallel lines are crossed by a straight transversal. One angle is $72^{\circ}$. The angle directly corresponding to it on the other parallel line is:
$72^{\circ}$
$108^{\circ}$
$18^{\circ}$
$36^{\circ}$
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WhyCorresponding angles between parallel lines are equal, so the angle is also $72^{\circ}$.
8Multiple choice · Easy
A net is folded to make a solid. A net of $6$ identical squares folds into which solid?
Cube
Square-based pyramid
Triangular prism
Cylinder
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WhySix identical squares fold to form a cube, which has $6$ square faces.
9Multiple choice · Easy
A ship sails due East. What is its bearing, measured clockwise from North?
$090^{\circ}$
$180^{\circ}$
$270^{\circ}$
$000^{\circ}$
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WhyBearings are measured clockwise from North and written with three figures. Due East is $090^{\circ}$.
10Multiple choice · Medium
What is the size of each interior angle of a regular octagon?
$135^{\circ}$
$45^{\circ}$
$120^{\circ}$
$144^{\circ}$
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WhyThe sum of interior angles is $(8-2)\times 180^{\circ}=1080^{\circ}$, so each interior angle is $\frac{1080^{\circ}}{8}=135^{\circ}$.
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