Geometry, Angles, and Shapes

Geometry is an important part of the SET 11+ maths papers. You will need to know the properties of 2D and 3D shapes, calculate angles, understand symmetry, and work with coordinates. On Stage 2, you must show your angle calculations step by step. This lesson covers all the geometry you need.

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Types of Angles

Angle type	Size	Example
Acute	Less than 90°	35°, 72°
Right angle	Exactly 90°	Corner of a square
Obtuse	Between 90° and 180°	120°, 155°
Reflex	Between 180° and 360°	210°, 300°

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Key Angle Rules

These rules come up again and again on the SET:

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

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Worked Example 1: Angles on a Straight Line

Two angles on a straight line are 118° and x°. Find x.

• 118 + x = 180
• x = 180 - 118 = 62°

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Worked Example 2: Angles in a Triangle

A triangle has angles of 47° and 68°. Find the third angle.

• 47 + 68 + x = 180
• 115 + x = 180
• x = 180 - 115 = 65°

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Isosceles Triangles

An isosceles triangle has two equal sides and two equal base angles.

Worked Example 3

An isosceles triangle has a top angle of 44°. Find each base angle.

• The two base angles are equal. Let each be x.
• 44 + x + x = 180
• 44 + 2x = 180
• 2x = 136
• x = 68°

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Angles in Polygons

The sum of interior angles of a polygon with n sides is: (n - 2) × 180°

Shape	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 ÷ number of sides.

Example: Each interior angle of a regular hexagon = 720° ÷ 6 = 120°.

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Properties of Quadrilaterals