volume_mute
Why Is the Angle Sum of a Quadrilateral 360°?
publish date: 2026/05/16 08:22:28.292781 UTC
volume_mute
A quadrilateral can be divided into triangles by drawing a diagonal, as shown below. Each triangle has an angle sum of 180°.
How many triangles is the quadrilateral divided into, and what is the total sum of its angle measures?
Correct Answer
2 triangles → 360°
Explanation
One diagonal divides the quadrilateral into 2 triangles. Since the sum of angle measures of any triangle is 180°: \[S = 2 \times 180° = 360°\]This matches the formula: \(S = (4-2) \cdot 180° = 2 \cdot 180° = 360°\).
Reference
Mathematics for college students