Primary 4 Maths: Angles
Types of angles, measuring and drawing with a protractor, angles on a straight line and vertically opposite angles — worked examples for the P4 Maths syllabus.
Most schools typically cover this topic in Term 3, around weeks 5–7 — though every school sets its own sequence.
Primary 4 is the year angles become measurable rather than just described. Children already know a right angle by sight from lower primary; P4 adds the vocabulary for acute (less than 90°), obtuse (between 90° and 180°) and reflex (between 180° and 360°) angles, the skill of measuring and drawing an angle accurately with a protractor, and two angle facts that do a lot of exam work: angles on a straight line add up to 180°, and where two straight lines cross, the angles opposite each other — vertically opposite angles — are equal. Note for parents comparing this to an older syllabus: the 2021 MOE Mathematics syllabus removed 8-point compass directions from the primary curriculum entirely, so it isn't part of P4 Angles any more — this page keeps to what's actually still taught.
The two angle facts above look like separate rules, but they're really the same idea used twice. A straight line is 180°, full stop — split it anywhere and the pieces still add to 180°. Two crossing lines make four angles out of two straight lines sharing a point, so the straight-line rule applies twice over, which is exactly why the opposite angles turn out equal. Seeing that connection, rather than memorising two disconnected facts, is what makes the harder questions below solvable.
P4 Angles: the mistakes to watch for
- Reading a reflex angle as its smaller "partner" on a protractor. A standard protractor shows two scales; for an angle that's obviously more than a straight line, the reading must be checked against 360° minus the other scale's reading, not read off automatically.
- Estimating a turn without checking against a right angle first. A quick mental check — "is this bigger or smaller than a square corner?" — catches acute/obtuse mix-ups before the protractor even comes out.
- Assuming angles "look" equal instead of using the straight-line or vertically-opposite rule. Diagrams in exam questions are rarely drawn to scale; the working has to come from 180° facts, not from eyeballing the picture.
- Forgetting a straight line only gives 180° once. In a question with three or more angles on one line, all of them together make 180° — not each pair, and not 360°.
P4 Angles: angle facts in the figure
P4 Angles: easy warm-ups
Easy: naming an acute angle
An angle measures 35°. What type of angle is it?
Show the worked solution
35° is less than 90°, so it is an acute angle.
Easy: naming an obtuse angle
An angle measures 92°. What type of angle is it?
Show the worked solution
92° is more than 90° but less than 180°, so it is an obtuse angle.
Easy: naming a reflex angle
An angle measures 210°. What type of angle is it?
Show the worked solution
210° is more than 180°, so it is a reflex angle.
Easy: naming a right angle
An angle measures exactly 90°. What type of angle is it?
Show the worked solution
An angle of exactly 90° is a right angle.
P4 Angles: exam-style questions
Exam: the other angle on a straight line
Two angles lie on a straight line. One of them is 128°. Find the other angle.
Show the worked solution
Angles on a straight line add up to 180°.
Other angle = 180° − 128° = 52°.
Exam: vertically opposite angles
Two straight lines cross at a point. One of the four angles formed is 65°. Find the sizes of the other three angles.
Show the worked solution
The angle vertically opposite 65° is also 65° (vertically opposite angles are equal).
Each angle next to the 65° angle is on a straight line with it: 180° − 65° = 115°. Both remaining angles are 115°.
Exam: three angles on a straight line
Three angles lie on a straight line. Two of them measure 40° and 65°. Find the third angle.
Show the worked solution
All three angles together make 180°.
Third angle = 180° − 40° − 65° = 75°.
Exam: one angle is twice the other
Two angles lie on a straight line. One angle is twice as large as the other. Find both angles.
Show the worked solution
Let the smaller angle be 1 part; the larger is 2 parts. Together, 3 parts = 180°, so 1 part = 60°.
The angles are 60° and 120°.
Check: 60° + 120° = 180°. ✓
Exam: finding all four angles at a crossing
Two straight lines cross at a point. One of the four angles formed is 72°. Find the other three angles.
Show the worked solution
The angle vertically opposite 72° is also 72°.
Each neighbouring angle is on a straight line with the 72° angle: 180° − 72° = 108°, and its vertically opposite angle is also 108°.
The four angles are 72°, 108°, 72° and 108°.
P4 Angles: PSLE-challenge preview
PSLE challenge: a right angle and two unequal parts
Three angles lie on a straight line. One of them is a right angle. Of the other two, the larger is twice the smaller. Find the two unknown angles.
Show the worked solution
The right angle uses 90° of the straight line, so the other two angles share 180° − 90° = 90°.
The smaller angle is 1 unit and the larger is 2 units, so 3 units = 90° and 1 unit = 30°.
The two unknown angles are 30° and 2 × 30° = 60°.
Check: 30° + 60° + 90° = 180°. ✓
PSLE challenge: two angles with a known difference
Two straight lines cross at a point. One of the four angles formed is 40° larger than the angle next to it. Find all four angles.
Show the worked solution
The two neighbouring angles are on a straight line, so they add to 180°. Take away the 40° difference and what's left is two equal smaller angles: 180° − 40° = 140°.
Smaller angle = 140° ÷ 2 = 70°. Larger angle = 70° + 40° = 110°.
Each angle has a vertically opposite partner of the same size, so the four angles are 70°, 110°, 70° and 110°.
Check: 70° + 110° = 180°, and 110° − 70° = 40°. ✓
PSLE challenge: two roads crossing at a signpost
Two straight roads cross at a signpost. One of the four angles between the roads is three times as large as the angle next to it. Find all four angles.
Show the worked solution
The angle and its neighbour lie on a straight line, so together they make 180°: 1 part + 3 parts = 4 parts = 180°, giving 1 part = 45°.
The angles are 45° and 3 × 45° = 135°, each repeated by its vertically opposite partner.
The four angles are 45°, 135°, 45° and 135°.
P4 Angles: how to practise this topic
Angles are one of the few P4 topics with a physical tool attached — a real protractor, lined up and read carefully, builds the same instinct that later lets a child sanity-check an algebra-heavy angle answer without one. Practise reading and drawing in both directions: given a measure, draw it; given a drawing, measure it. For the wider picture of what did and didn't change in P4–P6 Maths under the current syllabus, see the 2026 PSLE Maths syllabus changes.
What this topic covers
In the MOE Primary Mathematics syllabus, Primary 4 Angles includes the concepts below. (P4-M-08 is Test Paper's own topic code, not an MOE reference.)
- Types of angles (acute, right, obtuse, reflex)
- Measuring angles with a protractor
- Drawing angles
- Angles on a straight line
- Vertically opposite angles
- Angle word problems
Where to go next
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