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Primary - Stage 3 (Year 5 & 6) Stage 3 (Year 5 & 6) Angles

Angles on a straight line

20 practice questions 0 video lessons Theory + worked examples
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Theory

Angles that sit side by side on a straight line always add up to 180°. To find a missing angle, subtract the known angles from \(180^\circ\).

A straight line is a half turn, and a half turn is \(180^\circ\).

When two or more angles sit together along a straight line, with no gaps and no overlaps, their sizes add to \(180^\circ\).

To find a missing angle on a straight line, subtract the known angles from \(180^\circ\).

Two angles on a straight line A straight horizontal line with one ray rising from a point on it. The two angles, 130 degrees and 50 degrees, together make 180 degrees. 130° 50°
The two angles rest on one straight line, so \(130^\circ + 50^\circ = 180^\circ\).

Two angles on a line, one known.

StepWorking
Factangles on a line \(= 180^\circ\)
Known angle\(65^\circ\)
Subtract\(180^\circ - 65^\circ = 115^\circ\)

How to find an angle on a straight line

  1. Add the angles that are known.
  2. Subtract that total from \(180^\circ\).
  3. Check that all the angles on the line now add to \(180^\circ\).
Example 1 — One unknown
Two angles sit on a straight line. One is \(65^\circ\). Find the other.
Solution

\(180^\circ - 65^\circ = 115^\circ\).

The other angle is \(115^\circ\).

Example 2 — From a diagram
An angle of \(45^\circ\) sits on a straight line next to a missing angle. Find it.
Solution

\(180^\circ - 45^\circ = 135^\circ\).

The missing angle is \(135^\circ\).

Example 3 — Three angles
Three angles sit on a line. Two are \(35^\circ\) and \(65^\circ\). Find the third.
Solution

\(35^\circ + 65^\circ = 100^\circ\), then \(180^\circ - 100^\circ = 80^\circ\).

The third angle is \(80^\circ\).

Example 4 — Which pair fits
Could \(120^\circ\) and \(60^\circ\) sit together on a straight line?
Solution

\(120^\circ + 60^\circ = 180^\circ\).

They total \(180^\circ\), so yes.

Common pitfalls

The line must be straight. The fact only works when the outer arms make one straight line, not a bent one.
Add every angle on the line. If three angles sit on the line, all three add to \(180^\circ\), not just two.
180°, not 360°. A straight line is a half turn; the full turn of \(360^\circ\) is for angles right round a point.

Frequently asked questions

What do angles on a straight line add up to?

They add up to \(180^\circ\), because a straight line is a half turn.

How do you find a missing angle on a straight line?

Add the angles you know, then subtract from \(180^\circ\). For example \(180^\circ - 65^\circ = 115^\circ\).

Do three angles on a line still add to 180?

Yes. However many angles sit side by side on the line, together they add to \(180^\circ\).

What is the difference between 180 and 360 degrees here?

Angles on a straight line make \(180^\circ\), a half turn. Angles all the way round a point make \(360^\circ\), a full turn.