Example 1 · level 1
Three angles of a quadrilateral are 139°, 116° and 57°. Find the fourth angle (in degrees).
Show solution
- Sum of known angles = 139 + 116 + 57 = 312°.
- Fourth angle = 360° − 312° = 48°.
Answer: 48
CLASS 8 MATHS · UNDERSTANDING QUADRILATERALS
Angle sum of quadrilaterals and polygons
Angles of a quadrilateral add to 360°. An n-sided polygon has interior angles adding to (n − 2) × 180°, and exterior angles adding to 360°.
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Worked examples
Example 2 · level 2
The angles of a quadrilateral are in the ratio 3 : 3 : 3 : 1. Find the largest angle (in degrees).
Show solution
- 3x + 3x + 3x + 1x = 360° → 10x = 360° → x = 36°.
- Angles: 108°, 108°, 108° and 36°.
- Largest = 3 × 36 = 108°.
Answer: 108
Example 3 · level 3
Find each interior angle of a regular polygon with 8 sides (in degrees).
Show solution
- Exterior angle = 360° ÷ 8 = 45°.
- Interior angle = 180° − 45° = 135°.
Answer: 135