EDGE Math 8

Basic Postulates (2)

ANGLE MEASURE POSTULATES

When you use a protractor to measure angles, you are actually applying the Angle Measurement Postulate.

Postulate 8. Angle Measurement Postulate

To every angle, there corresponds a real number between 0 and 180.

The number being referred to in the Angle Measurement Postulate is the measure of an angle between 0° and 180°.

You can easily construct an angle using a protractor and the next postulate (the Angle Construction Postulate). The Angle Measurement Postulate and the Angle Construction Postulate ensure that the interior of an angle is measured.

Postulate 9. Angle Construction Postulate

Let

\vec{Q R}

be a ray on the edge of the half-plane H. For every number r between 0° and 180°, there is exactly one

\vec{Q P},

with point P in H, such that

m ∠ P Q R = r .

In the figure above, $∠ P Q R$ was constructed using a protractor and the Angle Construction Postulate.