IGCSE Math RevisionQuestion 1
Two angles on a straight line are \(3x\) and \(2x\).
Find \(x\).
Show the worked answer
- Angles on a straight line add to \(180°\): \(5x = 180\).
Answer: \(x = 36\)
Cambridge IGCSE Maths (0580) · Topic 4: Geometry · 4.6
Cambridge IGCSE Maths 0580 Angles Questions
Angles questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 10 questions
- 10 Core
- 8 non-calculator
- Free, no sign-in
What the syllabus asks
- 4.6 Angles Core
Angles on a line, at a point, vertically opposite, in triangles and quadrilaterals; Angles with parallel lines (corresponding, alternate, co-interior); Interior and exterior angles of polygons.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Angles questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
Two angles of a triangle are \(47°\) and \(68°\).
Find the third angle.
Show the worked answer
- \(180 - 47 - 68 = 65\)
Answer: \(65°\)
Question 3
A regular polygon has 10 sides. Find
(a) the size of each exterior angle (b) the size of each interior angle.
Show the answer and mark scheme
- B1 (a) 36°
- B1 (b) 144°
Answer: (a) \(36^\circ\) (b) \(144^\circ\)
Question 4
Work out the size of
(a) each exterior angle
(b) each interior angle
of a regular octagon.
Show the worked answer
- (a) Exterior angles add to \(360°\): \(360 \div 8 = 45°\).
- (b) Interior \(= 180° - 45° = 135°\).
Answer: (a) \(45°\) (b) \(135°\)
Question 5
A regular polygon has exterior angles of \(20°\).
How many sides does it have?
Show the worked answer
- The exterior angles of any polygon add to \(360°\): \(360 \div 20 = 18\).
Answer: \(18\)
Question 6
Work out the sum of the interior angles of a heptagon (\(7\) sides).
Show the worked answer
- A polygon with \(n\) sides splits into \(n - 2\) triangles: \((7 - 2) \times 180 = 900\).
Answer: \(900°\)
Question 7
Two parallel lines are crossed by a straight line. One of the angles formed is \(64^\circ\). Find
(a) the angle corresponding to it (b) the angle co-interior to it.
Show the answer and mark scheme
- B1 (a) 64°
- B1 (b) 116°
Answer: (a) \(64^\circ\) (b) \(116^\circ\)
Question 8
Five of the interior angles of a hexagon are \(110^\circ\), \(125^\circ\), \(130^\circ\), \(118^\circ\) and \(102^\circ\). Find the sixth angle.
Show the answer and mark scheme
- B1 angle sum 720°
- M1 720 − (110 + 125 + 130 + 118 + 102)
- A1 135°
Answer: \(135^\circ\)
Question 9
The interior angles of a pentagon are \(x°\), \(2x°\), \(100°\), \(110°\) and \(120°\).
Find \(x\).
Show the worked answer
- The angles of a pentagon add to \(3 \times 180 = 540°\).
- \(3x + 330 = 540\), so \(3x = 210\).
Answer: \(x = 70\)
Question 10
A line crosses two parallel lines. Two co-interior angles are \((2x + 10)°\) and \((3x - 30)°\).
Find \(x\).
Show the worked answer
- Co-interior angles add to \(180°\): \(5x - 20 = 180\).
- \(5x = 200\)
Answer: \(x = 40\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Geometry practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Geometry revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test angles?
Angles is on both tiers (syllabus 4.6), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more angles questions?
In the 0580 practice for topic 4 (Geometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.