11 self-marking GCSE practice questions on Sector angles at the centre, written specifically for AQA, Pearson, OCR across Foundation and Higher tier. Instant marking with full worked solutions on every question.
A few of the 11 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 11 markGrade 1-2
Two radii are drawn from the centre of a circle, splitting it into two sectors. One sector has a centre angle of 48°. What is the size of the centre angle of the other sector?
Show the worked solution
The angles at the centre of a circle always sum to 360°. If one sector's centre angle is 48°, the other sector's centre angle is 360−48=312°
What are the common mistakes in Sector angles at the centre?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Uses 360° for what is actually a part (arc/sector) of the circle
Used the full 360° angle at the centre instead of dividing it by the given fraction denominator
Uses the same given angle again instead of finding the new angle required
Repeated the given angle for the other sector instead of subtracting it from the full 360° at the centre
Trusts stated answer without recomputing
Assumed the sector must be a semicircle without actually setting up and solving the equation relating the FULL circle's circumference to the sector's perimeter (arc PLUS the two straight radii).
Quick answers about Sector angles at the centre
How many Sector angles at the centre practice questions are there?
There are 11 self-marking GCSE Maths questions on Sector angles at the centre, written for AQA, Pearson, OCR across Foundation and Higher tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Sector angles at the centre?
No. You can start practising Sector angles at the centre straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
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Question 21 markGrade 4-5
A circle has a sector with a curved edge that is exactly half the full circumference. What is the size of the angle at the centre of this sector?
Show the worked solution
The full angle at the centre of a circle is 360°. A sector whose arc is half the circumference has an angle at the centre of 360÷2=180°.
Question 34 marksGrade 7-8
OAB is a sector of a circle, centre O. OA = 6 cm, and AX is perpendicular to OB. The area of sector OAB is 6π cm².
Show that AX = 3√3 cm.
Question 43 marksGrade 8-9
A circle and a sector of the same circle both have radius r.
The circumference of the circle is equal to the perimeter of the sector.
Work out the size of angle x (the sector's angle at the centre). Give your answer in terms of π.