1.6 Describing Pairs of Angles Geometry 1.6 Describing Pairs of Angles
1.6 Describing Pairs of Angles June 1, 2019
1.6 Essential Question How can you describe complementary and supplementary angles and use these descriptions to find angle measures? 1.4 Perimeter and Area in the Coordinate Plane June 1, 2019
What You Will Learn Identify complementary and supplementary angles. Identify linear pairs and vertical angles. 1.6 Describing Pairs of Angles June 1, 2019
Recall from Last Lesson Sometimes, for clarity and convenience, we will use a single number inside the angle to name it. This is 1. 1 1.6 Describing Pairs of Angles June 1, 2019
More than One Angle 1 2 3 1.6 Describing Pairs of Angles June 1, 2019
Adjacent Angles Adjacent angles have the same vertex, O, and one side in common, OB. They share no interior points. A B C There are THREE angles: O AOB or BOA You cannot use the label O, since it would be unclear which angle that is. BOC or COB AOC or COA 1.6 Describing Pairs of Angles June 1, 2019
RST and VST are NOT adjacent angles. 1.6 Describing Pairs of Angles June 1, 2019
These angles are complementary AND adjacent. Complementary Angles Two angles are complementary if their sum is 90°. These angles are complementary AND adjacent. 65° 25° 1.6 Describing Pairs of Angles June 1, 2019
Complementary Angles Two angles are complementary if their sum is 90°. These angles are complementary AND NONADJACENT. Explain why: 30° 60° 1.6 Describing Pairs of Angles June 1, 2019
Supplementary Angles Angles are supplementary if their sum is 180°. These angles are adjacent AND supplementary (and a linear pair). 70° 110° 1.6 Describing Pairs of Angles June 1, 2019
Supplementary Angles Angles are supplementary if their sum is 180°. The angles are nonadjacent and supplementary. Explain why: 80° 100° 1.6 Describing Pairs of Angles June 1, 2019
Example 1 In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. 1.6 Describing Pairs of Angles June 1, 2019
Example 2 1.6 Describing Pairs of Angles June 1, 2019
Linear Pair Two adjacent angles are a linear pair if their noncommon sides are opposite rays. Common Side 1 & 2 are a linear pair. 1 2 A B C Noncommon sides 1.6 Describing Pairs of Angles June 1, 2019
Linear Pair Property The sum of the angles of a linear pair is 180°. 110° ? 70° 1.6 Describing Pairs of Angles June 1, 2019
Vertical Angles Two angles are vertical angles if their sides form two pairs of opposite rays. 3 1 2 1 & 2 are vertical angles. 4 3 & 4 are vertical angles. 1.6 Describing Pairs of Angles June 1, 2019
Vertical Angles Property Vertical Angles are congruent. ? 60° 60° 1.6 Describing Pairs of Angles June 1, 2019
Example 3 a. Are 1 and 2 a linear pair? Yes 1 2 3 4 5 b. Are 4 and 5 a linear pair? No c. Are 3 and 5 vertical angles? No d. Are 1 and 3 vertical angles? Yes 1.6 Describing Pairs of Angles June 1, 2019
Find the measure of the three angles. Example 4 Find the measure of the three angles. These angles form a linear pair. The sum is 180°. 130° 2 These are vertical angles, and congruent. 50° 1 50° 3 130° These angles are vertical angles. Vertical angles are congruent. 1.6 Describing Pairs of Angles June 1, 2019
Example 5 A Solve for x, then find the measure of each angle. B AEB and BEC form a linear pair. C D What do we know about the sum of the angles of a linear pair? The sum is 180°. 1.6 Describing Pairs of Angles June 1, 2019
Example 5 A 94° B Linear pair AEB and BEC means: (4x + 30) + (6x – 10) = 180 10x + 20 = 180 10x = 160 x = 16 (4x + 30)° E (6x – 10)° 86° 86° 94° C D Then AEB = 4(16) + 30 = 94 and BEC = 6(16) – 10 = 86 1.6 Describing Pairs of Angles June 1, 2019
Your Turn Work through these two problems. C 145° 1 2 3 (5x + 30)° A B 1. Find the measure of 1, 2, 3. 2. Find the measure of ABC. 1.6 Describing Pairs of Angles June 1, 2019
Your Turn Solutions 180° C (5x + 30)° (2x – 4)° 145° 35° A B 1 35° 3 2 mABC = 5(22) + 30 = 140° 1.6 Describing Pairs of Angles June 1, 2019
Essential Question How can you describe complementary and supplementary angles and use these descriptions to find angle measures? 1.4 Perimeter and Area in the Coordinate Plane June 1, 2019
Assignment 1.6 Describing Pairs of Angles June 1, 2019
1.6 Describing Pairs of Angles Day 2
Essential Question When two lines intersect, how do you know if two angles are congruent or supplementary and how do you use this information to find angle measures? 1.4 Perimeter and Area in the Coordinate Plane June 1, 2019
Vertical Angles are congruent. Quick Review 4 1 2 3 Vertical Angles are congruent. 1 2 & 3 4 1.6 Describing Pairs of Angles June 1, 2019
The angles of a Linear Pair are Supplementary Quick Review 4 1 2 3 The angles of a Linear Pair are Supplementary m1 + m4 = 180 m4 + m2 = 180 1.6 Describing Pairs of Angles June 1, 2019
Quick Review Two angles are supplementary if their sum is 180. Two angles are complementary if their sum is 90. 1.6 Describing Pairs of Angles June 1, 2019
Example 6 Solve for x, then find the angle measures. Solution: AEB and DEA are a linear pair. The sum of the angles in a linear pair is 180°. 6x + (3x + 45) = 180 9x = 135 x = 15 B 6(15) = 90° A 6x° E C (3x + 45)° 3(15) + 45 = 90° D 1.6 Describing Pairs of Angles June 1, 2019
Example 7 Solve for y, then find m1. Vertical angles are congruent, so: 5y – 50 = 4y – 10 y = 40 5(40) – 50 = 150° (5y – 50)° 30° 1 (4y – 10)° 150° 1 forms a linear pair with either of the 150° angles, so 1 is 30°. 1.6 Describing Pairs of Angles June 1, 2019
Example 8 Find the measure of each angle. 4x + 5 + 3x + 8 = 90 49° 41° This is a right angle, the angles are complementary. Their sum is 90°. 4(11) + 5 = 49° 3(11) + 8 = 41° 1.6 Describing Pairs of Angles June 1, 2019
Example 9 Find the value of each variable and the measure of each labeled angle. 5x + 4y = 130 5(14) + 4y = 130 70 + 4y = 130 4y = 60 y = 15 130° 50° (3x + 8)° (5x – 20)° 50° (5x + 4y)° 130° 3x + 8 = 5x – 20 -2x = -28 x = 14 3(14) + 8 = 50° 1.6 Describing Pairs of Angles June 1, 2019
Five Sample Problems For You To Do 1.6 Describing Pairs of Angles June 1, 2019
1. Solve for x. (4x + 40) (6x + 10) 1.6 Describing Pairs of Angles June 1, 2019
2. Solve for x. (12x – 12) (5x + 5) 1.6 Describing Pairs of Angles June 1, 2019
3. Solve for x. (x + 8) (7x + 2) 1.6 Describing Pairs of Angles June 1, 2019
4. Solve for x & y. (7x + 4) (9y + 3) (5y 5) (13x + 16) 1.6 Describing Pairs of Angles June 1, 2019
5. Solve for x. A is supplementary to B. mA = (2x + 10) mB = (3x 5) 2x + 10 + 3x 5 = 180 5x + 5 = 180 5x = 175 x = 35 1.6 Describing Pairs of Angles June 1, 2019
Essential Question When two lines intersect, how do you know if two angles are congruent or supplementary and how do you use this information to find angle measures? 1.4 Perimeter and Area in the Coordinate Plane June 1, 2019
Assignment 1.6 Describing Pairs of Angles June 1, 2019