Measuring angles in degrees

In a nutshell

An angle is formed when two lines meet at a shared point. Angles are measured in degrees ( $\degree$ ), which can be measured with a protractor.

Angles and measurement

The degree ( $\degree$ ) is the unit of measurement for angles. There are $90\degree$ in a right angle, and $360\degree$ in a full circle. A protractor is a tool used to measure how many degrees are in an angle.

Acute angles

Here are the steps for how to measure an acute angle with a protractor:

Procedure

1.	Place the midpoint of the protractor on the vertex of the angle.
2.	Line up one side of the angle with the zero line of the protractor (where the number $0$ appears).
3.	Read the degrees where the other side of the angle crosses the number scale.

Example 1

Maths; Geometry - properties of shapes; KS2 Year 5; Measuring angles in degrees

In the example above, the acute angle has a measurement of $\underline{40\degree}$ .

Obtuse angles

Here are the steps for how to measure an obtuse angle with a protractor:

Procedure

1.	Place the midpoint of the protractor on the vertex of the angle.
2.	Line up one side of the angle with the zero line of the protractor (where the number $0$ appears).
3.	Read the degrees of the other side of the angle, and subtract this value from $90\degree$ .
4.	Add the $90\degree$ to the previous value to find the overall obtuse angle.

Example 2

Maths; Geometry - properties of shapes; KS2 Year 5; Measuring angles in degrees

In the example above, the obtuse angle has a measurement of $\underline{110\degree}$ because:

$(90\degree - 70\degree) + 90\degree = \underline{110 \degree}$

Reflex angles

Here are the steps for how to measure a reflex angle with a protractor:

Procedure

1.	Place the midpoint of the protractor on the vertex of the angle.
2.	Measure the smaller angle on the other side of the reflex angle, with the same method as described above for an obtuse angle.
3.	Subtract this smaller angle from $360\degree$ to give the value of the reflex angle.

Example 3

Maths; Geometry - properties of shapes; KS2 Year 5; Measuring angles in degrees

In the example above, the reflex angle has a measurement of $\underline{320\degree}$ because:

$360\degree-40\degree=\underline{320\degree}$