Units of Measurement/Angle

The base unit of measurement for an angle is a degree (°) or a radian (c). A degree is 1/360th of a circle. 1 degree is equal to (pi/180) radians. 360 degrees is a full rotation and 180 degrees is equal to half a rotation or a straight line.

Common Values
30 degrees is when the sine function equals 0.5 and when cosine = sqrt(3)/2.

45 degrees is the non-right angles of a isoceles right triangle. It is also when the sine and cosine functions equal each other, equaling sqrt(2)/2. This is also half of a right angle.

60 degrees is the inverse of 30 degrees, where cosine equals 0.5 and sine equals sqrt(3)/2. It is also the number of degrees in an angle of an equilateral triangle. This is equal to π/3 radians.

90 degrees is the number of degrees in a right angle, and 4 right angles make a rectangle or a square. This is where sine equals 1 and cosine equals 0. This also equals π/2 radians.

180 degrees is a straight line, or what the internal angles add up to in a triangle, or what the exterior angles of any polygon add up to. It is also the number of degrees in a semi-circle. It is also equivalent to π radians.

270 degrees is 3/4ths of a rotation, or what 90 degrees clockwise is.

360 degrees is a full rotation or a circle. This equals 2π radians. This is also what the angles in a quadilateral add up to. 360 degrees per second is one Hertz

Formulas
The formula for an interior angle in a regular polygon is 180•(s-2)/s, where s is the number of sides in the polygon.