Primary 4 Angles Study Guide
Primary 4 angles in four short steps: naming an angle, measuring it with a protractor, drawing one of a given size and using angle sizes in a drawing, with something to try at each step.
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How are angles measured in degrees?
An angle's size is how far its arms open, counted in degrees.
Two arms meet at a point called the vertex. In Primary 4, your child measures the opening with a protractor and writes the size in degrees, such as 62°. A right angle is 90°, so a narrower opening reads less than 90° and a wider one reads more.
In this chapter, your child uses this to:
- name an angle with three letters, the vertex in the middle;
- measure an angle on the scale that starts at 0 on one arm;
- draw an angle of a given size with a ruler and protractor;
- use given angle sizes to find one part of a drawing.
Step 1
Naming angles with three letters
The middle letter is the vertex. An angle such as ∠UTV is named by a point on one arm, then the vertex, then a point on the other arm. ∠VTU names the same angle.
Tap two letters
Angles named: 0 of 3
Two rays, ML and MN, meet at M. Which is a name for the angle between them?
Step 2
Measuring angles with a protractor
Read the scale that starts at 0. Put the centre mark on the vertex and the base line along one arm. A protractor has two scales. Use the one whose 0 is on that arm, and check the reading against a right angle.
The base line is along one arm, and the 0 of the outer scale is on that arm. The other arm crosses 35 on the inner scale and 145 on the outer scale. What size is the angle?
Step 3
Drawing an angle of a given size
Draw one arm, then mark the size. Drawing reverses measuring. Draw the first arm with a ruler, put the protractor on it, mark a dot at the size you need and join the dot to the vertex.
Choose a size, then tap Next step
To draw ∠DEF = 120°, Arif puts the base line along EF. The 0 on EF is on the outer scale. Where does he mark his dot?
Step 4
Finding an unknown angle in a drawing
A part is the whole angle minus the other part. When a ray splits an angle in two, the two parts together make the whole angle. If you know the whole and one part, the other part is the whole minus that part.
Drag the slider
∠ABC = 95°. Ray BD lies inside it and ∠ABD = 40°. What is ∠DBC?
Primary 4 angles questions, worked step by stepHave a go on paper first. Open the hint, or reveal the working a line at a time.
Three rays, OA, OB and OC, start at the point O. Name the angle between OA and OC in two different ways.
- The arms OA and OC meet at O, so O is the vertex.
- The vertex letter goes in the middle: ∠AOC.
- Reversing the outer letters names the same angle: ∠COA. OB is not one of its arms.
Siti puts the centre mark of her protractor on E and the base line along ED. The 0 of the outer scale is on ED. Arm EF crosses 47 on the inner scale and 133 on the outer scale. What is the size of ∠DEF?
- E is the vertex, and the centre mark is on E.
- The outer scale starts at 0 on ED, so read the outer scale.
- EF crosses the outer scale at 133, so ∠DEF = 133°.
- Check: 133° is more than 90°, so ∠DEF should open wider than a right angle.
Draw ∠PQR = 72°, with QR as one arm.
- Draw QR with a ruler. Q is at one end.
- Put the centre mark on Q and the base line along QR.
- Find the scale that starts at 0 on QR. Count round it to 72 and mark a dot. Label it P.
- Join Q to P with a ruler. Measure ∠PQR again: it should read 72°, less than a right angle.
∠ABC = 126°. Ray BD is drawn between BA and BC so that ∠DBC = 49°. Find ∠ABD.
- ∠ABD and ∠DBC are the two parts of ∠ABC.
- ∠ABD = ∠ABC minus ∠DBC = 126° minus 49°.
- 126 minus 49 = 77, so ∠ABD = 77°.
Ravi measures two angles. For ∠x, the inner scale starts at 0 on the base arm, and the other arm crosses 64 on the inner scale and 116 on the outer scale. For ∠y, the outer scale starts at 0 on the base arm, and the other arm crosses 29 on the inner scale and 151 on the outer scale. How much greater is ∠y than ∠x?
- ∠x: the inner scale starts at 0, so ∠x = 64°.
- ∠y: the outer scale starts at 0, so ∠y = 151°.
- 151° minus 64° = 87°.
Step 5
Check yourself
Five short questions on naming, measuring and drawing. Nothing is saved; the answers point to the practice to do next.
1. In ∠KLM, which point is the vertex?
2. The 0 of the inner scale is on the base arm. The other arm crosses 81 on the inner scale and 99 on the outer scale. What is the angle?
3. An angle opens less than a right angle. Which reading could be its size?
4. To draw ∠ABC = 50° with BC as one arm, where does the centre mark go?
5. ∠PQR = 150°. Ray QS lies inside it and ∠SQR = 65°. What is ∠PQS?
Keep a protractor and ruler nearby. The steps on screen show each move, but the skill is in the hands. After Step 2, ask your child to measure a corner of a book or an open door on paper, saying aloud which scale starts at 0 before reading it. The whole guide takes about fifteen minutes.
Before each reading, ask "Is it more or less than a right angle?" That single question settles which of the two numbers is right. Let your child try each worked example on paper first, then open the working a line at a time.
More study guides
P4 Angles lessons and practice
1 lesson video and 22 questions across two subtopics, from Basic to Challenge, each with a worked solution.
Watch and practise →