Geometry and Measurement

Geometry and measurement questions test your understanding of shapes, angles, lengths, areas, and volumes. In the CEM 11+ exam, these questions may involve diagrams, or they may describe shapes in words and expect you to work without a picture. Being able to visualise shapes and recall key formulas is essential.

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Angles

Types of Angles

Type	Size	Example
Acute	Less than 90°	45°
Right	Exactly 90°	90°
Obtuse	Between 90° and 180°	120°
Straight	Exactly 180°	180°
Reflex	Between 180° and 360°	270°

Key Angle Facts

Rule	Total
Angles on a straight line	180°
Angles at a point	360°
Angles in a triangle	180°
Angles in a quadrilateral	360°
Interior angles of a polygon (n sides)	(n - 2) × 180°

Worked Example

Two angles on a straight line are 115° and x°. Find x.

x = 180 - 115 = 65°

Angles in Triangles