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

Construct angles

20 practice questions 0 video lessons Theory + worked examples
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Theory

To construct an angle, draw a baseline, place the protractor centre on its endpoint, mark the degree on the scale that reads zero along the baseline, then join the vertex to the dot.

The baseline is drawn first; one end is marked as the vertex.

The protractor centre sits on the vertex with the baseline along the zero line.

Mark a dot at the wanted degree on the scale whose \(0\) lies along the baseline, then join. For a reflex angle, draw \(360\) minus it.

Protractor measuring an angle of 60 degrees 0 180 20 160 40 140 60 120 80 100 100 80 120 60 140 40 160 20 180 0 60°
The baseline reads \(0\) on the outer scale. Mark a dot at \(60\), then join it to the vertex to construct a \(60^\circ\) angle.

Which mark to use depends on where the baseline sits.

Baseline scaleAngleMark
starts at \(0\)\(140^\circ\)\(140\)
starts at \(180\)\(65^\circ\)\(180-65=115\)
reflex\(300^\circ\)draw \(360-300=60\)

How to construct an angle

  1. Draw a baseline and mark one end as the vertex.
  2. Place the protractor centre on the vertex, baseline on the zero line.
  3. Mark the degree on the zero scale and join it to the vertex.
Example 1 — First step
What must be drawn first when constructing a \(60^\circ\) angle?
Solution

One arm must exist before the protractor is placed.

Draw a straight baseline with one end as the vertex.

Example 2 — Mark the degree
The baseline reads \(0\) on the outer scale. Where is the dot for \(140^\circ\)?
Solution

Read \(140\) on the scale that starts at \(0\) on the baseline.

Mark the dot at \(140\) on that scale.

Example 3 — Other scale
The baseline lies along the scale that starts at \(180\). What mark gives \(65^\circ\)?
Solution
\(180-65\)\(=\)\(115\)

Mark the dot at \(115\) on that scale.

Example 4 — Reflex angle
To construct a reflex angle of \(300^\circ\), what angle is drawn?
Solution
\(360-300\)\(=\)\(60\)

Draw \(60^\circ\); the turn the long way round is \(300^\circ\).

Common pitfalls

Skipping the baseline. The protractor can only be placed once one arm is already on the paper.
Using the wrong scale. Mark the degree on the scale whose \(0\) lies along the baseline; the other gives \(180\) minus the angle.
Reflex angles direct. A protractor reaches only \(180^\circ\), so for a reflex angle draw \(360\) minus it.

Frequently asked questions

How do you construct an angle with a protractor?

Draw a baseline, put the protractor centre on its endpoint, mark the degree on the scale that reads \(0\) along the baseline, then join the vertex to the dot.

What is drawn first?

The baseline. One arm must be on the paper before the protractor can be lined up, and its end becomes the vertex.

What if the baseline lies on the scale that starts at 180?

Mark \(180\) minus the angle. To construct \(65^\circ\), mark the dot at \(115\) on that scale.

How do you construct a reflex angle?

A protractor only reaches \(180^\circ\), so draw \(360\) minus the reflex angle. For \(300^\circ\), draw \(60^\circ\) and read the turn the long way round.