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Geometry questions on the CSSE 11+ maths paper test your knowledge of angles, 2D shapes, symmetry, and coordinates. The CSSE exam often combines geometry with reasoning — for example, asking you to work out an angle using several rules in sequence. This lesson covers all the key facts and methods you need.
| Angle type | Size | Description |
|---|---|---|
| Acute | Less than 90° | A sharp, small angle |
| Right angle | Exactly 90° | A square corner |
| Obtuse | Between 90° and 180° | A wide angle |
| Straight | Exactly 180° | A straight line |
| Reflex | Between 180° and 360° | More than a straight line |
You must learn these rules and apply them confidently in the exam.
| Rule | Fact |
|---|---|
| Angles on a straight line | Add up to 180° |
| Angles at a point | Add up to 360° |
| Angles in a triangle | Add up to 180° |
| Angles in a quadrilateral | Add up to 360° |
| Vertically opposite angles | Are equal |
Two angles on a straight line are 125° and x°. Find x.
A triangle has angles of 47° and 68°. What is the third angle?
| Triangle | Property |
|---|---|
| Equilateral | All three sides equal. All angles = 60°. |
| Isosceles | Two sides equal. Two base angles are equal. |
| Scalene | No sides equal. No angles equal. |
Worked Example: An isosceles triangle has a top angle of 50°. Find each base angle.
The sum of interior angles of a polygon with n sides is:
(n - 2) × 180°
| Polygon | Sides | Sum of interior angles |
|---|---|---|
| Triangle | 3 | 180° |
| Quadrilateral | 4 | 360° |
| Pentagon | 5 | 540° |
| Hexagon | 6 | 720° |
| Octagon | 8 | 1,080° |
For a regular polygon (all sides and angles equal):
Each interior angle = sum of angles ÷ number of sides
What is each interior angle of a regular hexagon?
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