Geometry & MeasuresStudy Notes

Worked Example 4: Missing Angle in Irregular Polygon

Part of Angles in PolygonsGCSE Mathematics

This study notes covers Worked Example 4: Missing Angle in Irregular Polygon within Angles in Polygons for GCSE Mathematics. Revise Angles in Polygons in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 7 of 9 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 7 of 9

Practice

12 questions

Recall

3 flashcards

Worked Example 4: Missing Angle in Irregular Polygon

A pentagon has angles of 105°, 115°, 98°, and 132°. Find the fifth angle.

Step 1 Find the sum of interior angles

Pentagon: n = 5

Sum = (5 − 2) × 180° = 3 × 180° = 540°

Step 2 Add known angles and subtract

Known angles = 105° + 115° + 98° + 132° = 450°

Fifth angle = 540° − 450° = 90°

Keep building this topic

Read this section alongside the surrounding pages in Angles in Polygons. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Angles in Polygons

What is the sum of the interior angles of a hexagon?

  • A. 540°
  • B. 720°
  • C. 900°
  • D. 360°
1 markfoundation

Explain how the formula (n − 2) × 180° for the sum of interior angles of a polygon is derived.

2 markshigher

Quick Recall Flashcards

Interior Angle Sum
Sum = (n - 2) × 180° for n-sided polygon
Exterior Angle Sum
Always 360° for any polygon

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