Interior angles of a quadrilateral
A quadrilateral is a polygon with 4 sides. A diagonal splits it into two triangles, and each triangle has angles adding to 180°.
Key idea / 要点
The four interior angles of a quadrilateral add up to 360°. (Using (n − 2) × 180° with n = 4 gives 2 × 180° = 360°.)
If you know three angles, subtract from 360° to find the fourth.
Exterior angles
At each vertex, an interior angle and its exterior angle lie on a straight line, so they add to 180°.
Key idea / 要点
The four exterior angles of any quadrilateral add up to 360°.
Worked example / 例题
Three interior angles of a quadrilateral are 90°, 85° and 110°. Find the fourth interior angle and its exterior angle.
Fourth interior angle = 360° − 90° − 85° − 110° = 75°.
Its exterior angle = 180° − 75° = 105°.
Check: 90° + 85° + 110° + 75° = 360°. Correct.
Remember / 记住
- Interior angles of a quadrilateral add to 360°.
- Exterior angles of a quadrilateral add to 360°.
- At any vertex, interior + exterior = 180°.