Angle Measurement

Overview

Every angle has a measure, and this lesson is about naming angles correctly, classifying them by their measure, and finding unknown measures. Two tools do most of the work: the Angle Addition Postulate, which splits one angle into the sum of its parts, and the angle bisector, which splits an angle into two congruent angles.

Vocabulary

Angle: A figure formed by two rays that share a common endpoint, called the vertex. An angle is named with three letters, with the vertex letter in the middle; it may be named by its vertex letter alone only when there is just one angle at that vertex.
Acute Angle: An angle whose measure is between 0° and 90°.
Right Angle: An angle whose measure is 90°.
Obtuse Angle: An angle whose measure is between 90° and 180°.
Straight Angle: An angle whose measure is 180°.
Adjacent Angles: Two angles that share a vertex and one common side, with no interior points in common — they sit next to each other with no gaps and no overlap.
Angle Bisector: A ray that divides an angle into two congruent angles, so the two parts have equal measures.

Main Ideas

Name an angle by its vertex: the middle letter of a three-letter name is always the vertex, and the other two letters lie on the angle's sides.
Classify by measure: acute (between 0° and 90°), right (90°), obtuse (between 90° and 180°), straight (180°).
Angle Addition Postulate: if point P is in the interior of ∠RST, then m∠RSP + m∠PST = m∠RST. The two angles being added must be adjacent.
An angle bisector creates two congruent angles, each measuring half of the whole angle.
With expressions, write the equation the picture describes — parts add to the whole, or the two halves are equal — then solve and substitute back for the measure the question actually asks for.