Use polygon angle sums
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Log in to continueExplain the triangle total and extend it to other plane polygons.
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Two interior angles of a triangle are 31° and 41°. What is the third?
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Answer: 108 degrees
- Triangle angles add to 180°.
- 180 − 31 − 41 = 108°.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Explain the triangle total and extend it to other plane polygons.
Read the official VCAA curriculum description (VC2M7M05)
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- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- VC2M7M05-C01The interior angles of a triangle in the plane total 180°. Subtract the known angles to find the missing one.
- VC2M7M05-C02A simple n-sided polygon can be triangulated into n − 2 triangles, giving a total of (n − 2) × 180°.
- VC2M7M05-C03Use the full 360° exterior turn of a convex polygon to recover a regular polygon’s side count, and relate adjacent interior and exterior angles.
- VC2M7M05-C04Demonstrating the triangle angle sum and communicating a generalisation to other plane shapes.
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Subskills
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Descriptor-derived subskills
- D01Complete a triangle’s angle totalThe interior angles of a triangle in the plane total 180°. Subtract the known angles to find the missing one.
- D02Divide a polygon into trianglesA simple n-sided polygon can be triangulated into n − 2 triangles, giving a total of (n − 2) × 180°.
- D03Connect exterior turns, side counts and interior anglesUse the full 360° exterior turn of a convex polygon to recover a regular polygon’s side count, and relate adjacent interior and exterior angles.