Report

Answers to Homework Page 40 5)Yes, they share a common side and vertex with no common interior points. 7)No they are supp 8)No they are comp 9)m<AOB or m<COD 10)<EOC 11) <EOC 12)<DOC 14)yes, they are marked 16)No they are not marked. 17)Yes, they form a line 18)Yes they are marked 19)No they are not marked 20)Yes they form a line 39)C 40)I 41)See Board 42)<WXY 43)<WXZ, <YXZ 44)39 Vertical Angles and Linear Pair September 8, 2011 • Objective: You will be able to identify and solve problems with vertical angles and linear pairs. • Bell Ringer: Solve for x 2x + 53 x+7 Angle Pairs • Vertical Angles: Two angles whose sides are opposite rays. The angles are congruent. (They form an X) • Linear Pair: Two angles that share a common ray and form a line. (The angles are supplementary) Example • <KPL and <JPL form a linear pair. If m<KPL = 2x + 24 and m<JPL = 4x + 36, what are the measures of the two angles? 2x + 24 + 4x + 36 = 180 Linear Pairs are Supplementary Combine Like Terms 6x + 60 = 180 6x = 120 Subtract 60 x = 20 Divide by 6 m<KPL = 2(20) + 24 = 64 Substitute 20 for x m<JPL = 4(20) + 36 = 116 Example • Solve for x and then find the measure of the two angles. 6x + 18 = 8x – 2 6x + 20 = 8x 20 = 2x 10 = x 6(10) + 18 = 78 Vertical Angles are Congruent Add 2 to both sides Subtract 6x from both sides Divide by 2 Substitute 10 for x Bisector • An angle bisector is a ray that divides two angles into two congruent angles. • Example: Ray CF bisects <ACE, find the value of x and the measure of <ACE. 5x = 2x + 24 3x = 24 x=8 5(8) + 2(8) + 24 = 80 Definition of a bisector Subtract 2x from both sides Divide both sides by 3 Substitute 8 for x Example 1 • Find the value of x. Answer: 23 Example 2 • Find the value of x. Answer: 20 Example 3 • Find the value of x. Answer: 8 Example 4 • Solve for x Answer: 35 Example 5 • Ray BT bisects <ABC, find the value of x Answer: 10 Example 6 • Solve for x Answer: 31 Example 7 • Ray BT bisects angle ABC. Solve for x. Answer: 5