Angles in Degrees — SAT Math Explained
The degree system for measuring angles, where a full rotation equals 360°, a straight angle equals 180°, and a right angle equals 90°.
The Core Idea
Degrees are the primary angle measurement system in basic geometry and trigonometry. The 360° full circle convention originated in ancient Babylonian astronomy, and remains the standard in everyday applications.
Angle Classifications
360°
180°
90°
0° < angle < 90°
90° < angle < 180°
180° < angle < 360°
Key Angle Facts
All interior angles of any triangle = 180°
All interior angles of any quadrilateral = 360°
(n - 2) × 180° where n = number of sides
Always 360° for any convex polygon
Adjacent angles on a straight line sum to 180°
Interior Angles Of Polygons
(3-2) × 180° = 180°
(4-2) × 180° = 360°
(5-2) × 180° = 540°
(6-2) × 180° = 720°
Degrees Vs Radians
Radians are the alternative measurement system used in higher mathematics and calculus. Conversion: 180° = π radians, so 1° = π/180 radians.
Common Errors to Avoid
Forgetting that the sum of all angles in a triangle is 180° (not 360°)
Using 360° instead of (n-2)×180° for polygon interior angle sums
Confusing exterior angles with interior angles
Practice: Angles in Degrees
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