2 VocabularyAn angle consists of two different rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle.
3 VocabularyAn angle is named with three points, just the vertex, or a number. An angle can be named with just the vertex only if it is the only angle with that particular vertex. The vertex is always the middle point when naming an angle with three points.
4 VocabularyWhen naming an angle, always remember to put a ∠ symbol in front. Otherwise you are naming a point or plane. To denote the measure of an angle, we write an “m” in front of the angle sign: m∠𝐴𝐵𝐶=90o
5 VocabularyAn acute angle has a measure between 0o and 90o A right angle has a measure of 90o An obtuse angle has a measure between 90o and 180o A straight angle has a measure of 180o
6 VocabularyTwo angle are congruent angles if they have the same measure. An angle bisector is a ray that divides an angle into two congruent angles.
7 VocabularyTwo angles are complementary angles if the sum of their measures is 90o. Two angles are supplementary angles if the sum of their measures is 180o.
8 VocabularyAdjacent angles are two angles that share a common vertex and side, but have no common interior points.
9 GUIDED PRACTICEfor Example 1In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles.1.Because 41° + 49° = 90°, FGK and GKL are complementary angles.Because 49° + 131° = 180°, HGK and GKL are supplementary angles.Because FGK and HGK share a common vertex and side, they are adjacent.
10 EXAMPLE 2Find measures of a complement and a supplementb. Given that is a supplement of 4 and m = 56°,find m 3.SOLUTIONb. You can draw a diagram with supplementary adjacent angles to illustrate the relationship.m 3 = 180° – m 4 = 180° –56° = 124°
11 GUIDED PRACTICEfor Examples 2 and 3LMN and PQR are complementary angles. Find the measures of the angles if m LMN = (4x – 2)° and m PQR = (9x + 1)°.
12 VocabularyTwo adjacent angles are a linear pair if their noncommon sides are opposite rays. The angles in a linear pair are supplementary angles.
13 VocabularyTwo angles are vertical angles if their sides form two pairs of opposite rays. Vertical angles are congruent to each other.
14 EXAMPLE 4Identify angle pairsIdentify all of the linear pairs and all of the vertical angles in the figure at the right.SOLUTIONTo find vertical angles, look or angles formed by intersecting lines.1 and are vertical angles.ANSWERTo find linear pairs, look for adjacent angles whose noncommon sides are opposite rays.1 and 4 are a linear pair and are also a linear pair.ANSWER
15 EXAMPLE 5Find angle measures in a linear pairTwo angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle.ALGEBRA
16 Angle Addition Postulate If P is in the interior of ∠𝑅𝑆𝑇, then the measure of ∠𝑅𝑆𝑇 is equal to the sum of the measures of ∠𝑅𝑆𝑃 and ∠𝑃𝑆𝑇.
17 VocabularyTo show that two angles in a diagram are congruent, we put an arc inside each angle.