An angle is a measure of turn between two lines that meet at a point. Angles are measured in degrees (°). There are six types you must know.
Example 1 — Identify and name these angles: 35°, 90°, 130°, 200°
35°
35° is less than 90° → Acute angle
90°
Exactly 90° → Right angle (shown with a small square)
130°
Between 90° and 180° → Obtuse angle
200°
Greater than 180° → Reflex angle
Example 2 — Using a protractor to measure an angle
Step 1
Place the centre hole of the protractor exactly on the vertex (the point where the lines meet).
Step 2
Rotate the protractor so that one arm of the angle lines up with the 0° baseline.
Step 3
Read the scale where the other arm crosses — use the inner scale if you started from the right, outer scale if from the left.
Step 4
Check your answer makes sense: if it looks acute, your reading should be under 90°.
Common mistake: Protractors have two scales (inner and outer). Always start reading from 0° on the correct scale for the side you placed your baseline. Reading the wrong scale gives an answer that adds to 180°.
✓ Quick Check 1 — Types of Angles
Question 1 of 10
Measuring and Drawing Angles
Accurate measurement is a key skill. You need to use a protractor correctly — both to read angles on diagrams and to draw angles of a given size.
Example 3 — Measure this angle correctly
Given
A diagram shows two lines meeting — one horizontal, one going up and to the right.
Step 1
Place the protractor centre on the vertex, align the 0° mark with the horizontal line (baseline).
Step 2
Read where the other line crosses the scale. Since the angle opens to the right from the baseline, use the inner (lower) scale.
Step 3
The reading is 65°. Check: the angle looks acute (less than 90°), and 65° < 90°. ✓
Example 4 — Draw an angle of 120°
Step 1
Draw a horizontal baseline and mark a vertex point at the left end.
Step 2
Place the protractor centre on the vertex, 0° on the baseline. Find 120° on the scale.
Step 3
Make a small mark at 120°. Remove the protractor and draw a line from the vertex to your mark.
Step 4
Label the angle 120°. Check: it should look obtuse (between a right angle and a straight line). ✓
Tip: Always estimate the angle before measuring. If it looks about 45°, a reading of 135° is wrong — you've used the wrong scale.
✓ Quick Check 2 — Measuring and Drawing Angles
Question 1 of 10
Angle Notation and Real-Life Angles
In geometry, we use a precise notation to identify angles. The symbol ∠ means "angle". When three letters are used, the middle letter is the vertex.
∠ABC = the angle at point B, measured between rays BA and BC
Example 5 — Interpreting angle notation ∠PQR = 48°
Step 1
Identify the vertex — it is the middle letter Q.
Step 2
The angle is formed between ray QP and ray QR, measured at Q.
Step 3
∠PQR = 48°. Since 48° < 90°, this is an acute angle.
Example 6 — Compass bearing to angle type
Given
A ship sails on a bearing of 210° from north.
Step 1
Bearings are measured clockwise from north (0°/360°).
Step 2
210° is between 180° and 360°, so measured from north this is a reflex angle.
Step 3
The ship is heading in a south-south-west direction.
Remember: ∠ABC = ∠CBA — the angle is the same whether you name it forwards or backwards. Only the middle letter (the vertex) matters.
✓ Quick Check 3 — Angle Notation and Real Life
Question 1 of 10
Practice: Identify the Angle Type
For each angle, type: acute, right, obtuse, straight, reflex, or full. Then click Check All.
#
Question
Answer
Result
1
47°
2
90°
3
135°
4
180°
5
270°
6
360°
7
15°
8
89°
9
200°
10
91°
⚠ Things to Watch Out For
Reading the wrong scale on a protractor: Protractors have two scales — inner and outer. Always check which scale starts at 0° for your angle. If the angle is acute (less than 90°), the answer must be less than 90°.
Measuring from the wrong end: The baseline of the angle must align with the 0° line on the protractor. Always check both arms of the angle are correctly positioned.
Reflex vs obtuse: Obtuse is between 90° and 180°. Reflex is greater than 180°. A reflex angle looks like "more than a straight line" — it goes the "long way round".
Estimating before measuring: Always estimate whether an angle is acute, right, obtuse or reflex BEFORE measuring. This prevents reading the wrong protractor scale.
Not starting from zero: If the protractor is not aligned at 0°, subtract the starting reading from the ending reading to find the actual angle size.