Section 1.3 – Measuring Angles

A protractor is used to measure angles.

Angles, like segments are measured in standard units called degrees. This is the unit of measure that results when a half circle is divided into 180 equal parts.

Measure of an angle: Suppose that the vertex, V, of is placed on the center point of a half-circle with coordinates from 0° to 180° so that and intersect on the half-circle. Let a and b be the coordinates of the intersections.

Then the measure of the angle, written as mis | a – b | or | b – a |.

If 2 angles have the same measure, then they are congruent and if 2 angles are congruent, then they have the same measure.

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Angle Addition Postulate: If point S is in the interior of , then

m+ m= m

Special Angle Pairs

Complementary angles are two angles whose measures have a sum of 90°. Each angle is called the complement of the other.

Supplementary angles are two angles whose measures have a sum of 180°. Each angle is the supplement of the other.

If the endpoint of a ray falls on the line so that 2 angles are formed, then the angles are known as a linear pair.

Linear Pair Property: If two angles form a linear pair, then they are supplementary.

Three Types of Angles

Right Angle – an angle whose measure is 90°

Acute Angle – an angle whose measure is < 90°

Obtuse Angle – an angle whose measure is > 90° and < 180°