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 10 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and 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°
Practice questions for Angles in Polygons
What is the sum of the interior angles of a hexagon?
Explain how the formula (n − 2) × 180° for the sum of interior angles of a polygon is derived.