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MathidiaMathematics Academy
Angle reasoning and constructions
Lesson 42 of 75
Easy practice

Angles in polygons

Objective. Calculate interior and exterior angles of polygons.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Angles in polygons develops a connected mathematical idea rather than an isolated trick. Build chains of geometric reasoning from angle facts. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Find the co-interior partner of 60°.

60
Illustrated card showing 60
  1. 1Identify the known information, the unknown and any conditions.
  2. 2Choose a diagram, table, graph or algebraic representation that exposes the structure.
  3. 3Apply the relevant rule one justified step at a time, keeping exact values where useful.
  4. 4Check by substitution, inverse reasoning or estimation. The result is 120°.

Answer: 120°

Concept mastery

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Practice

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Common mistake. A common error in angles in polygons is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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