Angles at a point is in the Primary 5 Angles chapter. The lesson film is the one Mathweave teaches this skill with in Primary 6, and the practice set below is chosen for Primary 5.
Find the point where the angles meet. At C, three angles meet: B C D, B C E and x.
Angles at a point add up to 360 degrees, one full turn.
The square's corner, angle B C D, is 90 degrees.
The triangle's angles at B and C are equal, so angle B C E is 180 minus 44, divided by 2, which is 68 degrees.
Subtract from the full turn: 360 minus 90 minus 68 is 202 degrees.
All the way round O is one full turn, 360 degrees. 214 and 63 are two of the three angles. 83 degrees is what is left. An angle bigger than 180 degrees is an angle that goes the long way round.
Practice questions with worked solutions
Question 1 is free to try. The other 3 open in the free trial, each with its full working.
∠BOC = 360° − 85° − 90° − 112° = 73° (angles at a point)
Answer: 73°
For parents
How do you solve P5 angles at a point questions?
This page covers angles at a point from the Primary 5 Geometry strand.
What your child learns here
This page covers angles at a point from the Primary 5 Geometry strand. Your child finds a missing angle where several rays meet at one point, and writes the reason beside each line of working.
All the angles round one point together make one full turn, 360°.
A small square at the point stands for 90°, so it is counted with the printed angles.
An angle whose arc sweeps the long way round is a reflex angle, more than 180° and less than 360°.
A reflex angle and the smaller angle between the same two arms add up to 360°.
A clock face shares its full turn into 12 equal parts of 30°, one for each hour.
Does the answer make sense?
Question 1 checks itself: 73° + 85° + 90° + 112° comes to 360°, exactly one full turn round O. Any angle found by taking the others off 360° must be more than 0°, and when its arc goes the long way round, the answer must be bigger than 180°.
How to practise these questions
Question 1, free to everyone, has four rays meeting at O: angle AOB is 85°, angle COD is a right angle drawn as a small square, and angle DOA is 112°, and your child finds angle BOC. The Basic questions train taking every known angle off 360°, reading the angle between the hands of a clock, and finding an angle marked the long way round. The Challenge question puts an isosceles triangle with its top corner at the point, so one angle comes from the triangle before the full turn is used. If your child gets stuck, open its worked solution and try the question again from Revision later. A multiple-choice Basic question shows four angles meeting at a point and asks which statement about their sizes is true; it has a written solution rather than a film.
Questions parents ask
Are angles at a point in the Primary 5 syllabus? Yes. Angles at a point sit in the Primary 5 Geometry strand beside angles on a straight line, vertically opposite angles and finding unknown angles.
What is a reflex angle? A reflex angle is more than 180° and less than 360°. Its arc goes the long way round the point, so your child finds it by taking the smaller angle between the same arms off 360°.
Why does the small square count as 90°? The small square is the sign for a right angle. It carries no number, yet it stands for 90° just as a printed 90° would, so it comes off the full turn with the others.
