Year 7 · Angles and polygons
Draw and measure lines and angles
Learn how to draw and measure angles accurately, then use angle facts at a point, on a straight line, between parallel lines and inside shapes to work out missing angles.
Definition
An angle measures a turn between two lines that meet at a point, and it is measured in degrees using a protractor. A full turn is 360 degrees, a half turn along a straight line is 180 degrees, and a quarter turn is a right angle of 90 degrees. Because these totals never change, a missing angle can be worked out by subtracting the angles you already know from the correct total, without measuring anything.
Why Do I Have to Learn This?
Angles measure turn, from door hinges to skate ramps. Reading them helps you build, draw and navigate accurately.
Key Rules:
- 1. To measure or draw an angle, place the protractor's centre on the point of the angle, line up the zero line with one arm, and read the scale that counts up from zero along that arm.
Remember:
- •A straight line is 180 degrees and a full turn is 360: every missing angle comes from subtracting what you know from the right total.
Don’t Forget...
- •Reading the wrong protractor scale, so a 50 degree angle is recorded as 130 degrees. A protractor carries two scales running in opposite directions; the correct one starts at zero on the arm you lined up, and a quick check that an acute angle reads under 90 catches the error.
- •Using 360 degrees for angles on a straight line, or 180 degrees for angles around a point. A straight line is only half a turn, so its total is 180; starting the subtraction from the wrong total makes every missing angle wrong by the same amount.
- •Marking alternate or corresponding angles as equal when the two lines are not parallel. The Z and F angle facts are true only for parallel lines, shown by matching arrows on the diagram; without them the two angles can be any sizes at all.
Acute angle
An angle smaller than 90 degrees.
An angle of 45° is acute.
Worked Example:
Three angles meet around a point. Two of them are 145 degrees and 90 degrees. Work out the third angle.
Angles around a point add up to 360 degrees.
Add the angles you know: 145 + 90 = 235 degrees.
Subtract from the full turn: 360 - 235 = 125 degrees.
Answer: 125 degrees
Why It Works:
A full turn is defined as 360 degrees, so angles that fit together around a point must total exactly 360, and a straight line is half a turn, which is why its angles total 180. Any straight-sided shape can be split into triangles from one corner: an n-sided shape splits into n - 2 triangles of 180 degrees each, which is exactly where the formula (n - 2) x 180 comes from.
Another Example:
Four angles of a pentagon are 100 degrees, 110 degrees, 120 degrees and 90 degrees. Work out the fifth angle.
A pentagon has 5 sides, so it splits into 5 - 2 = 3 triangles: its angle sum is 3 x 180 = 540 degrees.
Add the four known angles: 100 + 110 + 120 + 90 = 420 degrees.
Subtract from the angle sum: 540 - 420 = 120 degrees.
Answer: 120 degrees
Animated Example:
Free Draw and measure lines and angles Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Before this: Shape (Year 6) · Next: Symmetry and reflection (Year 8)
Let’s Practise the Concept
Step 1 of 3
Put the angles in order
Tap them from smallest to largest.
In order so far: nothing yet