Chapter 1

Basics of Geometry

Section 6Angles and Their Measures

An __angle__ consists of two rays that have the same endpoint.

The rays are the __sides__ of the angle.

The endpoint is the __vertex__ of the angle.

In the photograph at the right, the sides of <BAC are AB and AC. The vertex of <BAC is point A.

You can also write <BAC as <CAB. Notice the middle letter in the name of the angle is always the vertex of the angle.

You can write simply <A if there are no other angles that have this same vertex.

Example 1: Name Angles

Name the angles in the figure.

<PQS (<SQP)

<SQR (<RQS)

<PQR (<RQP)

Checkpoint: Name Angles

Name the angles in the figure.

The measure of an angle is written in units called __degrees__.

The measure of <A is denoted by __m<A__.

Example 2: Measure Angles

Use a protractor to approximate the measure of <BAC.

m<BAC = 50*

Two angles are __congruent angles__ if they have the same measure. In the diagram below, the two angles have the same measure, so <DEF is congruent to <PQR. You can write <DEF ≅ <PQR.

Angles are classified as __acute__, __right__, __obtuse__, or __straight__, according to their measures. Angles have measures greater than 0° and less than or equal to 180°.

Example 3: Classify Angles

Classify each angle.

obtuse right acute

Example 4: Add Angle Measures

Find the measure of <PTM.

<PTN + <NTM = <PTM

30 + 40 = <PTM

70* = <PTM

Checkpoint: Add and Subtract Angle Measures

looking for the whole add; looking for the part subtract

Find the measure of <ABC.