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Year 5 Maths Angles

Construct angles

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Theory

To construct (draw) an angle, draw a baseline, put the protractor's centre on its end, mark a dot at the angle on the scale that starts at \(0\) on the baseline, then join the dot to the vertex. This Year 5 maths page shows those steps, how the two scales can trip you up, and how to draw a reflex angle by drawing \(360^\circ\) minus it instead.

The baseline is the first arm of the angle. One end of it is the vertex.

The protractor's centre mark goes on the vertex and its base line along the baseline. Mark the angle on the scale that reads \(0\) at the baseline.

If you use the other scale by mistake, you draw \(180^\circ\) minus the angle you wanted.

A reflex angle is more than \(180^\circ\). A protractor only reaches \(180^\circ\), so draw the angle \(360^\circ - \text{reflex angle}\); the reflex angle is the larger angle on the outside of the arms.

Marking 80 degrees for a construction A protractor with its centre on the end of a baseline that points right. A green dot is marked at 80 on the inner scale, which reads 0 on the baseline. 180160140120100806040200 020406080100120140160180 centre on the vertex
Step 3: dot at \(80\) on the scale that reads \(0\) on the baseline.
Finished 80 degree angle The finished angle: the baseline and a second arm drawn from the vertex through the dot, making an angle of 80 degrees. 80°
Step 4: join the vertex to the dot with a ruler: \(80^\circ\).
Reflex angle of 240 degrees Two arms making an angle of 120 degrees inside. The reflex angle of 240 degrees on the outside is marked with a red arc. 240°
Draw \(360 - 240 = 120^\circ\); the outside angle is \(240^\circ\).

Construction facts:

\[ \text{wrong scale} \;\Rightarrow\; 180^\circ - \text{angle} \]
wrong scale gives 180− angle
\[ \text{reflex angle} = 360^\circ - \text{angle drawn} \]
reflex angle =360− angle drawn
Sharp pencil, exact dot. A thick line or a careless dot can put the angle out by a few degrees.
Check by measuring. When you have finished, measure the angle again with the protractor.

How to construct an angle up to 180°

  1. Draw a straight baseline with a ruler and mark one end as the vertex.
  2. Place the protractor centre on the vertex with its base line along the baseline.
  3. Mark a dot at the angle on the scale that reads \(0\) on the baseline.
  4. Remove the protractor and join the vertex to the dot with a ruler.
  5. Label the angle.

How to construct a reflex angle

  1. Subtract the reflex angle from \(360^\circ\).
  2. Construct that smaller angle.
  3. Mark the reflex angle on the outside of the arms.
Example 1 — Order the steps
Put these steps for constructing \(80^\circ\) in order. P: join the vertex to the dot. Q: draw a baseline. R: mark a dot at \(80\). S: place the protractor centre on the vertex.
Solution

Q, S, R, P.

Example 2 — Which scale?
Eli places the protractor so that the baseline is at \(180\) on the scale he is using. To draw \(25^\circ\), which number on that scale must he mark?
Solution
\(180 - 25\)\(=\)\(155\)
180−25=155

\(155\) on that scale (which is \(25\) on the other scale).

Example 3 — Reflex angle
What angle do you draw with the protractor to construct a reflex angle of \(240^\circ\)?
Solution
\(360 - 240\)\(=\)\(120^\circ\)
360−240=120

\(120^\circ\); the reflex angle is the \(240^\circ\) outside it.

Example 4 — More reflex angles
What angle is drawn with the protractor for
(i) \(310^\circ\)?
(ii) \(200^\circ\)?
Solution
\(360 - 310\)\(=\)\(50^\circ\)
\(360 - 200\)\(=\)\(160^\circ\)
50,160

(i) \(50^\circ\)
(ii) \(160^\circ\)

Example 5 — Wrong scale
Ava meant to draw \(75^\circ\), but she marked \(75\) on the scale that reads \(180\) at the baseline. What angle did she draw?
Solution
\(180 - 75\)\(=\)\(105^\circ\)
180−75=105

\(105^\circ\).

Example 6 — Find the mistake
Tom put the end of the protractor's straight edge (not the centre mark) on the vertex to draw \(45^\circ\). Why is his angle wrong?
Solution

The scales are measured from the centre mark. With the centre off the vertex, the dot is in the wrong place, so the angle will not be \(45^\circ\).

Common pitfalls

Using the wrong scale. Check: an angle under \(90^\circ\) should look smaller than a square corner.
Centre mark not on the vertex. Line up the small centre mark, not the corner of the protractor.
Drawing the reflex angle with the protractor. Draw \(360^\circ\) minus it, then mark the outside angle.
Freehand second arm. Use a ruler to join the vertex to the dot.

Frequently asked questions

What do you draw first?

A straight baseline with one end marked as the vertex.

Where does the protractor go?

With its centre mark on the vertex and its base line along the baseline.

Which scale do you use?

The one that reads \(0\) where the baseline is.

How do you draw a reflex angle?

Draw \(360^\circ\) minus the reflex angle, then mark the outside angle. For \(240^\circ\), draw \(120^\circ\).

How can you check your construction?

Measure the angle you drew with the protractor.

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