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°
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.
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.