1.1.3 Measuring and Constructing Angles (continued)
Angles can be classified by their measures. There are four types of angles with measures between 0° and 180°: straight, obtuse, right, and acute angles. A straight angle is also a line; its measure is 180°. An obtuse angle measures between 90° and 180°. The measure of a right angle is exactly 90°. A small box placed in an angle’s interior, near its vertex, is used to indicate that the angle is a right angle. All angles with a measure that is less than that of a right angle (so, less than 90°) are called acute angles. In this example, a protractor is placed over a given figure and then used to find m ∠ BOD (read as “the measure of angle BOD ”). The vertex of ∠ BOD is O . So, the center of the protractor is placed on O . To use the protractor to find m ∠ BOD , place it so that 0° is on one of the angle’s sides, ray OB . Then identify the degree measure on the protractor that corresponds with placement of the angle’s other side, ray OD . Since OD passes through the protractor at 65°, m ∠ BOD = 65°. The measure of ∠ BOD is less than 90°. Thus, ∠ BOD is an acute angle. The Segment Addition Postulate states that when a segment is divided into two parts, the sum of the lengths of those two parts is equal to the length of the whole segment. The Angle Addition Postulate relates the parts of an angle to each other in the same way that the Segment Addition Postulate relates the parts of a segment to each other. By the Angle Addition Postulate, when an angle is divided into two parts, the sum of the measures of those two parts is equal to the sum of the whole angle.
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