Construct angles
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.
Which mark to use depends on where the baseline sits.
| Baseline scale | Angle | Mark |
|---|---|---|
| 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
- Draw a baseline and mark one end as the vertex.
- Place the protractor centre on the vertex, baseline on the zero line.
- Mark the degree on the zero scale and join it to the vertex.
One arm must exist before the protractor is placed.
Draw a straight baseline with one end as the vertex.
Read \(140\) on the scale that starts at \(0\) on the baseline.
Mark the dot at \(140\) on that scale.
| \(180-65\) | \(=\) | \(115\) |
Mark the dot at \(115\) on that scale.
| \(360-300\) | \(=\) | \(60\) |
Draw \(60^\circ\); the turn the long way round is \(300^\circ\).
Common pitfalls
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.