The fold

Primary 5 Angles study guide: the whole chapter, step by step

About this subtopic

The fold 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.

Lesson video, with the working

Angles in a Folded Figure

2 min 34 s

The question shows first; its working is written as the film explains it.

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Today's question

ABCD is a rectangular piece of paper. It is folded along the dotted line AE. Angle AED is 58°. Find angle x.

  1. Angle x is 26°.

Ans: 26°

How to solve it
  1. The crease is a line of symmetry. The corner that moved is D prime, and a fold never changes the size of an angle.
  2. Find angle D A E in triangle A D E: corner D is a right angle, and angle A E D is 58 degrees.
  3. Subtract: angle D A E is 180 minus 90 minus 58, which is 32 degrees.
  4. The folded copy, angle D prime A E, is also 32 degrees. Folded angles are equal.
  5. Corner A is a right angle shared by three angles, so x is 90 minus 32 minus 32, which is 26 degrees.

The right angle at D is the right angle at D prime. A fold is a change of place, not a change of size.

Practice questions with worked solutions

Question 1 is free to try. The other 4 open in the free trial, each with its full working.

Basic

Intermediate

Challenge

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4 more questions, each with its full working.Answers checked, progress kept, wrong ones come back in revision. No card needed.

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Question 1 of 5 · Basic · free to tryABCD is a rectangular piece of paper. Corner D is folded along the crease…ABCD is a rectangular piece of…

ABCD is a rectangular piece of paper. Corner D is folded along the crease AE, where E is on DC, so that D lands at D' on the paper. Angle D'AE = 24°. Find angle AED.

°

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Video solution · 1 min 10 s

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Working

  1. ∠DAE = ∠D'AE = 24° (folded angles are equal)
  2. ∠AED = 180° − 90° − 24° = 66° (angle sum of triangle ADE)

Answer: 66°

For parents

How do you solve P5 folded paper angle questions?

Folding questions use the Primary 5 angle facts on a rectangle or parallelogram of paper.

What your child learns here

Folding questions use the Primary 5 angle facts on a rectangle or parallelogram of paper. Your child spots the pair of equal angles a fold makes, then finds the unknown angle with straight-line, right-angle and triangle facts.

  • A fold moves part of the paper but leaves every angle on that part the same size.
  • The crease sits between an angle and its folded copy, and the two angles are equal.
  • A corner that moves gets a prime mark, so D′ is the new place of corner D.
  • Each corner of a rectangular sheet is 90°, and its folded copy is 90° as well.
  • Angles along one straight edge of the paper add up to 180°, and so do the angles of each triangle.
Does the answer make sense?

Triangle ADE in Question 1 has angles of 90°, 24° and 66°, which add up to 180°. The fold makes angle DAE 24° too, so the two angles at A on either side of the crease match, as a fold must make them.

How to practise these questions

Question 1, free to everyone, folds corner D of rectangle ABCD along the crease AE so that D lands at D′. Angle D′AE is 24°, and your child finds angle AED. The Basic questions train using the fold's equal pair once, inside one triangle or along a straight edge. The Intermediate questions chain the fold with a right-angled corner, a straight edge or the parallel sides of a parallelogram. The Challenge question uses the fold's equal angles more than once. If the fold gets confusing, open its worked solution and trace which angle moved where.

Questions parents ask

Is paper folding in the Primary 5 syllabus? Folding is not an outcome of its own. These questions use the Primary 5 outcomes on angles, triangles and four-sided figures, set on a sheet of paper that has been folded.

What does the prime mark on D′ mean? D′ is read "D prime". It names where corner D lands after folding, so the angle at D′ equals the angle at D.

Should my child unfold the paper in their head? Yes, it helps. Picturing the flap folded back shows each moved angle lying on top of the angle it came from.