Page 1 · Introduction
The language of shapes
Geometry is the maths of shapes, lines and angles. Year 7 builds a toolkit of angle facts that let you work out missing angles without measuring — just by reasoning. It’s more like a puzzle than a calculation.
The big ideaA few angle facts unlock most questions: angles on a straight line add to 180°, angles round a point add to 360°, and the angles in a triangle add to 180°.
💡No protractor needed here — we use the angle facts to reason out the answers. We start simple.
On the real testWhere this appearsAngle facts and geometry reasoning are a key part of Year 7 maths, and set up everything from triangles to coordinate geometry later on.
Page 2 · Types of angle
Naming angles
Angles are named by size: an acute angle is less than 90°, a right angle is exactly 90°, an obtuse angle is between 90° and 180°, and a straight angle is 180°.
What type of angle is 45°?
Less than 90°, so it is acute.
Acute
What type of angle is 120°?
Between 90° and 180°, so it is obtuse.
Obtuse
Page 3 · Angles on a line
Adding to 180°
Angles that sit together on a straight line always add up to 180°. So if you know one, you can find the other.
Two angles on a straight line. One is 110°. What is the other?
180 − 110 = 70°.
70°
One angle on a line is 45°. Find the other.
180 − 45 = 135°.
135°
Page 4 · Angles at a point
Adding to 360°
Angles that meet all the way round a point add up to 360°.
Three angles round a point are 120°, 100° and one more. Find it.
120 + 100 = 220. 360 − 220 = 140°.
140°
Four equal angles meet at a point. How big is each?
360 ÷ 4 = 90°.
90°
Page 5 · Triangles
Adding to 180°
The three angles inside any triangle always add up to 180°. Know two, and you can find the third.
A triangle has angles 60° and 70°. Find the third.
60 + 70 = 130. 180 − 130 = 50°.
50°
A right-angled triangle has one angle of 30°. Find the third.
Right angle is 90°. 90 + 30 = 120. 180 − 120 = 60°.
60°
Level 1 · Easy
Warm up
Naming angles. Tap to check.
1. What type of angle is 90°?
A Acute
B Right
C Obtuse
D Straight
Exactly 90° is a right angle.
2. What type of angle is 30°?
A Acute
B Right
C Obtuse
D Straight
Less than 90° is acute.
3. What type of angle is 150°?
A Acute
B Right
C Obtuse
D Straight
Between 90° and 180° is obtuse.
Level 2 · Medium
Building up
Angles on a line.
1. Angles on a line: one is 120°. Find the other.
180 − 120 = 60°.
2. Angles on a line: one is 90°. Find the other.
180 − 90 = 90°.
3. Angles on a line: one is 35°. Find the other.
180 − 35 = 145°.
Level 3 · Hard
Getting tougher
Angles at a point and in triangles.
1. Angles round a point: 150°, 90° and one more. Find it.
150 + 90 = 240. 360 − 240 = 120°.
2. A triangle has 50° and 60°. Find the third angle.
50 + 60 = 110. 180 − 110 = 70°.
3. Two equal angles on a line. How big is each?
180 ÷ 2 = 90° each.
Level 4 · Challenge
Challenge
Multi-step angle reasoning.
1. A triangle has a right angle and a 40° angle. Find the third.
90 + 40 = 130. 180 − 130 = 50°.
2. Angles round a point: three equal angles. How big is each?
360 ÷ 3 = 120°.
3. An isosceles triangle has a top angle of 40°; the two base angles are equal. Find each base angle.
180 − 40 = 140 for the two equal angles. 140 ÷ 2 = 70° each.
Page 10 · Well done
You’ve finished Geometry & Angles
You can now name angles and use the key facts — angles on a line (180°), round a point (360°) and in a triangle (180°) — to reason out missing angles. This logical approach is exactly what Year 7 geometry rewards.
RememberStraight line = 180°. Round a point = 360°. Triangle = 180°. Know all but one angle, and you can always find the last.
🎉Great work getting through all four tiers. Try another module next — every one builds a different skill.
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