Primary 5 Angles Study Guide

Five short steps through the Primary 5 angle properties, each with a figure your child can step through or turn. Worked examples and a five-question check follow.

Start here

What are angles on a straight line and angles at a point?

Half a turn is 180° and a full turn is 360°.

The angles that sit side by side on a straight line make half a turn, so they add up to 180°. All the angles round one point make a full turn, 360°. When two straight lines cross, the angles facing each other are equal. Your child finds an unknown angle with one of these facts, and writes the fact in brackets beside the line.

In this chapter, your child learns to:

  • name an angle with three letters, the vertex in the middle;
  • use angles on a straight line and vertically opposite angles;
  • find an angle at a point, even one that goes the long way round;
  • use the two angles between a pair of parallel sides;
  • find angles on a sheet of paper after a fold.

XOY is a straight line. Find ∠POY.

  1. ∠XOP + ∠POY = 180°
    (angles on a straight line XOY)
1

Step 1

Angles on a straight line

The name says which angle; the bracket says which fact. In ∠DOB the middle letter, O, is the vertex where the two arms meet, and D and B sit on the arms. Read backwards, ∠BOD is the same angle. Every angle standing on one side of a straight line at the same point adds up to 180°, so the unknown one is 180° minus the others.

Tap Next step

AOB is a straight line. ∠AOC = 48° and ∠COD = 75°. Find ∠DOB.

ABCDO48°75°?
We want ∠DOB: O is the vertex in the middle, and D and B are on its two arms. Tap Next step.
Try it

In the figure above, which name is the same angle as ∠DOB?

▶ Watch the lesson: Straight lines and opposite anglesPractise 6 questions →
2

Step 2

Vertically opposite angles

Where two straight lines cross, facing angles match. Two crossing lines make four angles at one point. Each angle and the one beside it sit on a straight line, so they add up to 180°. The angle across the crossing, facing it, is always the same size. Turn the line and see the pairs stay equal.

Drag the slider

PRQS65°115°65°115°
  1. ∠QOR = 180° − 65° = 115°
    (angles on a straight line POR)
  2. ∠ROS = ∠POQ = 65°
    (vertically opposite angles)
  3. ∠SOP = ∠QOR = 115°
    (vertically opposite angles)
∠POQ is 65°, so ∠ROS, facing it, is 65° too. Each neighbour is 180° minus 65°, which is 115°.
Try it

Straight lines EG and FH cross at O, and ∠EOF = 38°. Going round O, which list gives ∠EOF, ∠FOG, ∠GOH and ∠HOE?

▶ Watch the lesson: Straight lines and opposite anglesPractise 6 questions →
3

Step 3

Angles at a point

Every angle round one point shares the same 360°. Find the point where the angles meet and list each one. When a square and a triangle meet at a corner, the square gives a right angle and the triangle gives its own angle. An angle whose curve is drawn outside the figure goes the long way round, so it is more than 180°.

Tap Next step

ABCD is a square. In triangle BCE, EB = EC and ∠BEC = 52°. Find ∠x.

ABCDE52°x
x is at C, and its curve runs round the outside, more than half way. Tap Next step.
Try it

OA, OB and OC meet at O. ∠AOB = 228°, going the long way round, and ∠BOC = 75°. Find ∠COA.

▶ Watch the lesson: Angles at a pointPractise 5 questions →
4

Step 4

Angles between parallel sides

Begin at the angle that has a number, then follow the sides. Matching arrowheads mark two sides as parallel. At the two ends of a side that runs from one to the other, the pair of angles between the parallel sides adds up to 180°. A line from a corner splits that corner into two parts. The last line is usually the angle sum of a triangle.

Tap Next step

In trapezium ABCD, AB is parallel to DC. ∠ABC = 122°, ∠BCE = 35° and ∠EDC = 38°. Find ∠DEC.

ABCDE122°35°38°?
∠DEC is in triangle DEC, which has only one other angle given, 38°. Tap Next step.
Try it

In trapezium WXYZ, WX is parallel to ZY and the diagonal XZ is drawn. ∠WXY = 126° and ∠XZY = 47°. Find ∠YXZ.

▶ Watch the lesson: Following the parallel routePractise 3 questions →
5

Step 5

Folded paper angle questions

Folding moves an angle but keeps its size. The crease is a line of symmetry, so the part that folds over lands exactly on a copy of itself. A corner that moves gets a prime mark: D′ is corner D in its new place. A right angle stays a right angle. Find the angle before the fold first, then use its copy beside the crease.

Tap Next step

Rectangle ABCD is a sheet of paper, folded along the dotted line AE. ∠AED = 64°. Find ∠x.

ABCDE64°
Corner D is about to fold over the dotted crease AE. Tap Next step to fold it.
Try it

Rectangle ABCD is folded along AF, with F on BC. Corner B lands at B′ inside the rectangle. ∠BAF = 31°. Find ∠B′AD.

▶ Watch the lesson: The foldPractise 5 questions →

Primary 5 angles questions, worked step by stepSay which fact each line needs before you open it. A hint and the working wait below.

Straight lineBasic

KM and LN are straight lines that cross at O. Ray OP lies between OL and OM. ∠KOL = 64° and ∠LOP = 70°. Find ∠POM and ∠MON.

∠KOL, ∠LOP and ∠POM stand on the straight line KOM. ∠MON faces ∠KOL.
  1. ∠POM = 180° − 64° − 70° = 46° (angles on a straight line KOM)
  2. ∠MON = ∠KOL = 64° (vertically opposite angles)
Answer: ∠POM = 46°, ∠MON = 64°
At a pointIntermediate

OA, OB, OC and OD meet at O. ∠AOB = 96°, ∠COD is a right angle, and ∠BOC = ∠DOA. Find ∠BOC.

Minus the two angles you know from 360°. Two equal angles share what is left.
  1. ∠BOC + ∠DOA = 360° − 96° − 90° = 174° (angles at a point)
  2. ∠BOC = 174° ÷ 2 = 87°
  3. Check: 96° + 87° + 90° + 87° = 360°
Answer: 87°
Parallel sidesIntermediate

ABCD is a trapezium with AB parallel to DC. E is a point inside it. ∠BAD = 104°, ∠ADE = 30° and ∠DCE = 51°. Find ∠DEC.

∠BAD and ∠ADC are the two angles between the parallel sides at the ends of AD.
  1. ∠ADC = 180° − 104° = 76° (angles between the parallel sides AB and DC)
  2. ∠EDC = 76° − 30° = 46° (the two parts of ∠ADC)
  3. ∠DEC = 180° − 46° − 51° = 83° (angle sum of triangle DEC)
Answer: 83°
The foldChallenge

ABCD is a rectangular sheet of paper. Corner C is folded along BF, where F is on DC, and lands at C′ inside the sheet. ∠DFC′ = 48°. Find ∠ABC′.

∠BFC and ∠BFC′ are folded copies, and with ∠DFC′ they sit on the straight edge DC.
  1. ∠BFC + ∠BFC′ = 180° − 48° = 132° (angles on a straight line DFC)
  2. ∠BFC = 132° ÷ 2 = 66° (folded angles are equal)
  3. ∠CBF = 180° − 90° − 66° = 24° (angle sum of triangle BCF)
  4. ∠C′BF = ∠CBF = 24° (folded angles are equal)
  5. ∠ABC′ = 90° − 24° − 24° = 42° (right angle of a rectangle)
Answer: 42°
Mixed practiceChallenge

Straight lines AB and CD cross at O. BD is joined so that OB = OD, and BD is extended to E. ∠AOC = 48°. Find ∠ODE.

∠BOD faces ∠AOC. Triangle OBD has two equal sides.
  1. ∠BOD = ∠AOC = 48° (vertically opposite angles)
  2. ∠ODB = (180° − 48°) ÷ 2 = 66° (base angle of isosceles triangle OBD)
  3. ∠ODE = 180° − 66° = 114° (angles on a straight line BDE)
Answer: 114°
6

Step 6

Check yourself

Five figures described in words. Each reply names the practice set that fits it.

1. XYZ is a straight line, and rays YP and YQ are on the same side of it. ∠XYP = 67° and ∠PYQ = 58°. Find ∠QYZ.

2. Straight lines EF and GH cross at O. ∠EOG = 116°. Find ∠FOH.

3. Four angles meet at a point: 104°, 92°, 75° and ∠y. Find ∠y.

4. PQRS is a parallelogram. ∠QPS = 71°. Find ∠PSR.

5. Corner A of rectangle ABCD folds over the line DG, where G is on AB, and lands at A′ inside. ∠ADG = 22°. Find ∠A′DC.

0/5
Answer all five to see where to practise next.
For parents

Using the figures. Before your child taps Next step, ask: which fact comes next, and which angle will it give? Then tap and compare. Each figure takes a few minutes, and the slider in Step 2 is worth a minute of turning.

On paper, ask for the angle's name, the working and the fact in brackets on one line, such as (angles at a point). Writing the fact down is how your child checks each step, and it shows which angle can be found next.

More study guides

Before this: PercentageNext: Properties of TrianglesPrimary 4 Angles study guidePrimary 3 Angles study guidePrimary 3 Perpendicular and Parallel Lines study guidePrimary 5 Parallelogram, Rhombus and Trapezium study guide
Lessons and practice

P5 Angles lessons and practice

5 lesson videos and 19 questions across five subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →