11 plus Angles questions

What an Angles question looks like

An Angles question in the 11 plus asks for a size in degrees, or for the name of an angle, and offers five options. Almost all of them rest on a small set of facts: a right angle is 90°, angles on a straight line add up to 180°, angles that meet round a point add up to 360°, the angles inside a triangle add up to 180°, and the angles inside a four-sided shape add up to 360°. Nothing in this part of the eleven plus asks your child to name a shape or count its lines of symmetry, which is a different sort of maths question. Here the answer is a number of degrees, or the word acute, right, obtuse, straight or reflex.

Two thirds of the questions carry a figure drawn on screen: an angle with an arc across it, a four-sided shape with three corners labelled, a spinner cut into equal sectors, a clock face. The rest are pure text, and a few of those give your child a claim made by another child to judge rather than a sum to do.

Example one: how many 30° angles fit together to make a straight line?

The options are 12, 4, 9, 6 and 3.

A straight line is 180°. If every angle is 30°, the question is really asking how many thirties are in 180. Count up in thirties, or divide: 180 ÷ 30 = 6. The answer is 6, and six lots of 30 does come to 180.

The tempting wrong option is 12. That is 360 ÷ 30, the answer for a full turn rather than a straight line. A child who has just met “angles round a point make 360°” reaches for the bigger number without rereading the question. The words to slow down on are “straight line”.

Example two: the angles on a straight line are n°, 2n° and 30°. What is n?

The options are 90, 60, 50, 45 and 30.

There are three angles this time and they still have to make 180°, so n + 2n + 30 = 180. The two n parts make 3n, so 3n + 30 = 180. Take the 30 off both sides: 3n = 150. Then share that between the three parts: n = 50. The three angles are 50°, 100° and 30°, which add to 180°, so it works.

The trap here is 60, and it catches good arithmetic. It comes from 180 ÷ 3, sharing the whole 180° as though all three angles were the same size. They are not: one is fixed at 30°, and that 30° has to come out before anything is shared. Testing 60 shows it at once, since 60 + 120 + 30 = 210, too big for a straight line.

Example three: the reflex angle between the hands of a clock

The clock shows exactly 8 o’clock. The angle wanted is the reflex one, the big way round: starting at the minute hand on the 12 and going clockwise past the 1, 2, 3 and on until it reaches the hour hand on the 8. The options are 120°, 270°, 240°, 320° and 210°.

A clock face is a full turn cut into twelve equal parts, so each hour mark is 360 ÷ 12 = 30° from the next. Now count the steps the arc passes: 12 to 1, 1 to 2, and so on up to 7 to 8. That is 8 steps of 30°, so the angle is 8 x 30 = 240°.

The option that tempts is 120°, the small way round: the other 4 steps, 4 x 30 = 120. It is the angle most children picture between two hands, and it is a good angle, just not the one asked for. The check is quick, because the two ways round must make a full turn, and 240 + 120 = 360.

How to answer it

1. Decide which total you are working with before you touch a number. 90° for a right angle, 180° for a straight line or the inside of a triangle, 360° for a full turn, for angles meeting round a point, or for the inside of a four-sided shape.
2. Add up every angle you already know, in one go. Write that total down rather than holding it in your head.
3. Take that total away from the total in step 1. That is the missing angle.
4. If the question asks for the big way round, take the small angle away from 360°. If the angles are equal, or given as a ratio, divide instead: count the equal parts, then share the total between them.
5. Put your answer back with the other angles and add them up. A straight line has to come to 180° and a point to 360°. If it does not, you know before you have chosen an option.

Common mistakes

• Starting from the wrong total. Using 360° for angles on a straight line gives 360 - 115 = 245° instead of 65°, and using 180° round a point does the same in reverse. Answers exactly 180 out are always among the options.
• Stopping after one subtraction. With 45°, 90° and a missing angle on a line, taking away only the 45 gives 135, which sits there waiting to be picked. Every known angle has to come off.
• Giving back a number that was already in the question. If one angle is given as 115°, then 115° will be one of the five options. It is the answer to nothing, and it catches a child who has run out of time.
• Sharing before subtracting. When one angle is fixed and the others are equal, the fixed one comes out of the total first. Divide too early and every share is too big.
• Guessing at the names. Reflex is not always 270°, and an angle just over a right angle, like 95°, is still obtuse. Obtuse means anything between 90° and 180°, however close to 90°.

How to practise 11 plus Angles questions

The quickest gain is not more questions, it is the totals said out loud until they are automatic: 90, 180, 360, triangle 180, four-sided shape 360. A child who has to stop and work out which total applies has already lost the time the question was meant to take. After that, the useful practice is mixed: a naming question, then a missing angle on a line, then one round a point, so that choosing the total stays part of the job.

11+ Daily has an Angles project inside its 11 plus maths practice, covering naming and estimating angles, missing angles on a line and round a point, angles inside triangles and four-sided shapes, and the ones that arrive dressed as a spinner or a clock. Every question is original to 11+ Daily, nothing is a past paper, nothing is licensed from another publisher, and the bank is re-checked in rounds. If you are working out how much time to give it, we have written about how much 11 plus practice a child needs each day.

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