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Section 5.1 · Geometry and measure

A sum of 360°

Know that the angles around a point total 360°, derive that the angles of a quadrilateral also total 360°, and use both to calculate missing angles.

6 teaching slides 116 practice questions Worked answers for every question

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2 · Key words

angleA measure of turn, given in degrees.
degree (°)The unit for measuring angles; a full turn is 360°.
angles at a pointAngles that meet at one point and fill a full turn.
straight lineAngles on one side of a straight line total 180°.
quadrilateralA shape with four straight sides.
acute angleAn angle less than 90°.
right angleAn angle of exactly 90°.
obtuse angleAn angle between 90° and 180°.
reflex angleAn angle greater than 180°.

3 · Summary of the sectionrevise from this

  • A full turn is 360°, so the angles around a point total 360°.
  • A straight line is half a turn, so the angles on a straight line total 180°.
  • The angles of a triangle total 180°.
  • The angles of a quadrilateral total 360° — draw one diagonal and it splits into two triangles.
  • To find a missing angle: add the ones you know, then subtract from the total.
  • Acute < 90°; right = 90°; obtuse is between 90° and 180°; reflex > 180°.
  • Check your answer is sensible: does it look about the right size in the diagram?
PDFPrintable worksheet All 116 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons5 videos

Math Antics - Angles & Degrees

American mathantics

Where degrees come from and why a full turn is 360. Start here if angles are new.

Angles in a full circle

British corbettmaths

Angles that meet at a point: add what you know, subtract from 360°.

Angles in a Straight Line

British corbettmaths

The 180° half-turn rule, with the reasons written out as Cambridge expects.

Angles in Quadrilaterals

British corbettmaths

Shows *why* a quadrilateral totals 360° by splitting it into two triangles — this is the derivation objective 7Gg.11 asks for.

Missing Angles — worked answers

British stretchcorbettmaths

Full worked solutions to a mixed exercise. Try the questions first.

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4 · Practice116 questions, easiest first

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5.2 Intersecting lines