Interior angles of a triangle

Use the fact that the interior angles of any triangle sum to 180 degrees, together with the angle properties of isosceles and equilateral triangles, to find unknown angles and to judge whether a set of angles can form a triangle.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • GM5-5
New NZC (2026)
  • NZC26-P4-GEO-SHP-P-Y10-01
  • NZC26-P3-GEO-SHP-K-Y7-03
  • NZC26-P3-GEO-SHP-K-Y7-04
  • NZC26-P3-GEO-SPR-K-Y7-03

Resources

  • Alpha textbook: Angles in a triangle, Ex 25.02, pg 415-416
  • Dr Austin Maths - Angles in Triangles Practice GridQuestions PDF · Answers
  • Dr Austin Maths - Angles in Triangles and Quadrilaterals Practice GridQuestions PDF · Answers
  • CorbettMaths on angles in trianglesQuestions PDF · Answers
  • Beta: Exercise 18.04, pgs 345 & 346
  • Beta: Exercise 18.05, pgs 347 & 348

Terminology

  • triangle
  • scalene triangle
  • isosceles triangle
  • equilateral triangle

Task goals

  • Find a missing angle in a scalene, isosceles, equilateral, or right-angled triangle from a labelled diagram, using the 180-degree angle sum.
  • Use the equal base angles of an isosceles triangle to find both remaining angles from one given angle.
  • Explain why every equilateral triangle has three 60-degree angles.
  • Set up and solve an equation when one or more interior angles are given as an algebraic expression.
  • Find all three angles when they are given as a ratio, and name the triangle using angle language.
  • Decide whether a given set of angles can form a triangle, and explain an incorrect claim using the angle-sum rule.

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Interior angles of a triangle

Interior angles of a triangle

Know

The interior angle sum of a triangle is 180°; for a quadrilateral, it is 360°.

Statement▸
Year 7 · Geometry · Spatial reasoning
NZC26-P3-GEO-SPR-K-Y7-03

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