The idea in brief. The angles round a point fill one full turn, 360°, and one of them may be the one that goes the LONG way, past half a turn, bigger than 180°. It is still one angle and it is still the rest of the turn, so it is found and used by exactly the same subtraction: `360° −` the angles you can see. The arc says which way round; the size confirms it, because only the long way can be more than 180°. In the lesson. An angle bigger than one hundred and eighty degrees is an angle that goes the long way round.
Lesson video, with the working
Angles at a point
2 min 50 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
ABCD is a square and BCE is a triangle. EB is the same length as EC and angle BEC is 44°. Find angle x.
Angle x is 202°.
Ans: 202°
Example 1
OA, OB and OC meet at the point O. Angle AOB = 214° and angle BOC = 63°. Find angle y.
Angle y is 83°.
Ans: 83°
How to solve it
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 6 open in the free trial, each with its full working.
1 sector = 360° ÷ 12 = 30° (the 12 equal hours round the face)
smaller angle = 4 × 30° = 120° (four sectors of the full turn)
Answer: 120°
For parents
How do you solve angles at a point questions in P6?
All the angles around one point make a full turn of 360°.
What your child learns here
All the angles around one point make a full turn of 360°. On this Primary 6 page that fact meets right-angle boxes, crossing lines and angles marked on the outside of a figure, where the angle is bigger than 180°.
Use the property that angles at a point add up to 360°.
Include every angle round the point, including a right angle shown only as a small square.
Recognise an angle bigger than 180° by the way its mark goes the long way round, and find it as what is left of the full turn.
Combine angles at a point with other facts, such as the equal angles of an isosceles triangle or the 90° corner of a rectangle.
Does the answer make sense?
When the angle's mark goes the long way round, the answer must be more than 180° but less than 360°; when the mark sits on the short side, it must be less than 180°. Your child can see which applies from the curve of the mark on the figure.
How to practise these questions
Basic questions train adding angles round a point to 360 degrees and finding the one that is missing, including an angle measured the long way round. Intermediate questions add squares, rectangles and isosceles triangles meeting at a shared corner. Challenge questions hide the starting angle inside a triangle, or turn two shapes so that a gap opens between them. When the angles round a point will not add up, read the written step-by-step solution together.
Questions parents ask
What is an angle that goes the long way round? It is an angle bigger than 180° and smaller than 360°, measured the long way round a point. The syllabus covers angles at a point, which add up to 360°, so its size is 360° minus the angle on the other side.
Is angles at a point in the P6 syllabus? Angles at a point is listed in the MOE syllabus before Primary 6, under Geometry. In Primary 6 it is used inside composite figures with squares, rectangles, triangles and other quadrilaterals.
Why do angles at a point use 360° and not 180°? 180° is a half turn: the angles on one straight line. Angles all the way round a point make a full turn, which is 360°.
