Primary 5 maths · Geometry · About 12 minutes
Use angles on a straight line
Locate the common vertex, the given lines and the complete turn being filled.
Start the interactive lesson →Open practice activity
What you will learn
- Use angles on a straight line
Models used: number sentences, stories, diagrams.
Before you start
Use the turn you already know
A straight line makes a half-turn. That whole turn is 180 degrees.
The straight line is the whole half-turn. The coloured arcs show its two parts.
A straight line makes a half-turn. That whole turn is 180 degrees.
The unknown angle must fill exactly the part of the straight turn that the known angle does not use.
The straight line is the whole half-turn. The coloured arcs show its two parts.
The blue part uses 60 degrees. The orange part must fill the space left over.
The unknown angle must fill exactly the part of the straight turn that the known angle does not use.
The straight line is the whole half-turn. The coloured arcs show its two parts.
Subtract the known part from the whole turn.
180° − 60° = 120°
The unknown angle must fill exactly the part of the straight turn that the known angle does not use.
What did the picture help us see?
Subtract the known part from the whole turn.
Worked example: A new example, together
Angles 140° and x° form a straight angle. Find x.
The straight line is the whole half-turn. The coloured arcs show its two parts.
Locate the common vertex, the given lines and the complete turn being filled.
The component angles exactly fill 180 degrees.
The straight line is the whole half-turn. The coloured arcs show its two parts.
The complete turn here is 180°.
The unknown angle must fill exactly the part of the straight turn that the known angle does not use.
Angles 140° and x° form a straight angle. Find x.
40 degrees
The straight line is the whole half-turn. The coloured arcs show its two parts.
Subtract the known angle: 180 − 140.
The unknown angle must fill exactly the part of the straight turn that the known angle does not use.
The straight line is the whole half-turn. The coloured arcs show its two parts.
x = 40°.
The unknown angle must fill exactly the part of the straight turn that the known angle does not use.
The straight line is the whole half-turn. The coloured arcs show its two parts.
Check the result against the question we started with.
140 + 40 = 180°.
We found 40 degrees. The component angles exactly fill 180 degrees.
Common mistakes to discuss
- Any two angles make a straight line. Angles on a straight line total 180°, so the partner of 60° is 120°.
Check your understanding
- Use angles on a straight line
- justify an unknown angle with the stated angle relationship
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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