How are Angles Measured?

When we measure an angle, we do not measure the lengths of the sides. Two angles with completely different side-lengths may be congruent or equal angles.

The way to measure an angle is to measure the magnitude of its "openness". This measurement indicates how far the sides are away from one another in a circular path.

In the figures below, the measure of angle RDS is greater than the measure of angle PAQ, since it is more open than angle PAQ.  It does not matter that the sides of angle PAQ are longer than the sides of angle RDS.