Measurements of Common Angles

Straight Angle
A full rotation (or full angle) is defined to be $$360^\circ$$ or $$2\pi$$ rad.

Since lines are straight, it therefore follows that from any point on a line, the angle between one side of the line and the other is one half of a full rotation. Therefore, the measurement of a straight angle is $$\frac{360^\circ}{2}=180^\circ$$ or $$\frac{2\pi}{2}$$ rad$$=\pi$$ rad.

Right Angle
Since right angles are equal to one half of a straight angle, the measurement of a right angle is $$\frac{180^\circ}{2}=90^\circ$$ or $$\frac{\pi}{2}$$ rad.