Angles

Geometry questions often show a figure with one mystery angle and a little letter like x marking it. You are not expected to measure it — you work it out using a few angle facts. This is a P5 topic, and these three rules cover a huge number of "find the unknown angle" questions. Learn them and a confusing figure turns into a quick subtraction.

Parents: ask your child to name the angle fact they will use before they reveal. The "Method tip" boxes name the exact rule a PSLE marker rewards — quoting the rule earns marks.

By the end you'll be able to use angles on a straight line, angles at a point, and vertically opposite angles to find unknown angles. Let's measure up.

Angles on a straight line

When angles sit together along a straight line, they make a half turn. The rule is: angles on a straight line add up to 180 degrees. So if one part is known, subtract it from 180 to find the rest.

For example, if a straight line is split into an angle of 110 degrees and an unknown angle x, then x = 180 − 110 = 70 degrees. The two angles together must complete the half turn of 180 degrees.

Drag the known angle and watch the unknown one fill the rest of the straight line.

🔬

Find the unknown angle

🤔 Predict first: Angles on a straight line add up to…

180 degrees360 degrees90 degrees

Angles at a point

When angles meet all the way around a single point, they make a full turn. The rule is: angles at a point add up to 360 degrees. Add up the angles you know and subtract from 360 to find the missing one.

For example, three angles meet at a point: 150 degrees, 120 degrees and an unknown x. Then x = 360 − 150 − 120 = 90 degrees. All the angles around the point must complete the full turn of 360 degrees.

Vertically opposite angles

When two straight lines cross, they make four angles. The two angles opposite each other across the crossing are equal — these are vertically opposite angles.

For example, if two lines cross and one angle is 70 degrees, the angle directly opposite it is also 70 degrees, with no calculation needed. The angles next to it lie on a straight line, so each is 180 − 70 = 110 degrees.

Putting the rules together

Harder figures need two rules in a row. You might use vertically opposite angles to copy one angle across, then angles on a straight line to find a neighbour. Work one step at a time, naming the rule at each step.

For example, two lines cross and one angle is 50 degrees. Its vertically opposite angle is also 50 degrees, and an angle next to it on the straight line is 180 − 50 = 130 degrees. Each step uses a single, named rule.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. Two angles lie on a straight line. One is 130 degrees. What is the other?

   50 degrees230 degrees70 degrees

2. Angles at a point are 90 degrees, 90 degrees and x. What is x?

   180 degrees270 degrees90 degrees

3. Two straight lines cross. One angle is 55 degrees. What is the angle directly opposite it?

   125 degrees55 degrees35 degrees

4. Three angles on a straight line are 40 degrees, 70 degrees and x. What is x?

   70 degrees110 degrees250 degrees

5. Four angles meet at a point: 80 degrees, 100 degrees, 80 degrees and x. What is x?

   80 degrees100 degrees120 degrees

6. Two lines cross. One angle is 35 degrees. What is the size of an angle right next to it on the straight line?

   35 degrees145 degrees55 degrees

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