Measuring and Drawing Angles

What you will learn

• Measure an angle with a protractor.
• Draw an angle of a given size.
• Estimate an angle first to avoid reading the wrong scale.

Before you start: you should know the types of angle. See Angles.

The idea

A protractor is a half-circle with a scale from $0^\circ$ to $180^\circ$. Most have two scales, one running each way, so you must choose the right one.

Measuring step by step

1. Estimate first. Is the angle smaller or bigger than a right angle?
2. Put the centre of the protractor on the vertex.
3. Turn the protractor so one arm lies along the $0$ line.
4. Follow the scale that starts at $0$ along that arm up to the other arm.
5. Check the answer against your estimate.

Drawing an angle

To draw $50^\circ$: draw a straight arm, put the protractor on one end, mark $50^\circ$ on the scale that starts at $0$, then join the mark to the end of the arm.

Reflex angles

A protractor only goes to $180^\circ$. To measure a reflex angle, measure the other side and take it from $360^\circ$. If the short side is $110^\circ$, the reflex angle is $360 - 110 = 250^\circ$.

Worked examples

Example 1: Choose the scale

An arm lies along the $0$ on the right-hand scale. The other arm points between $100$ and $120$, at the mark for $115$ on the left-hand scale. What is the angle?

1. Estimate: the angle looks acute, less than $90^\circ$.
2. The scale that starts at $0$ on this arm is the right-hand one, which reads $65$ at the same mark.

Answer: $65^\circ$

Example 2: Draw $50^\circ$

1. Draw a line and mark the vertex at one end.
2. Place the protractor with its centre on the vertex and the line on $0$.
3. Mark $50$ on the scale that starts at $0$.
4. Join the vertex to the mark.

Answer: an acute angle of $50^\circ$.

Example 3: Reflex

Measure the reflex angle whose short side is $75^\circ$.

1. $360 - 75 = 285$.

Answer: $285^\circ$

Tip: an acute angle should read under $90$ and an obtuse angle over $90$. If not, you used the wrong scale.

Why it matters

Measuring angles is a skill used in construction, map reading, art and sport. It also builds your sense of what an angle of $30^\circ$, $60^\circ$ or $90^\circ$ looks like.