Do Now (Turn on laptop to my calendar) Simplify each expression – (x + 20) – (3x – 10) Write an algebraic expression for each of the following more than twice a number 4. 6 less than half a number 70 – x 190 – 3x 2n + 4

Success Criteria:  I can identify special angle pairs  I can identify geometric relationships  I can use angle pairs to find angle measures Today 1. Do Now 2.Check HW #3 3.Vocabulary 4.Lesson HW #4 6.Complete iReady Do Now (Turn on laptop to my calendar) Simplify each expression – (x + 20) – (3x – 10)

adjacent angles linear pair complementary angles supplementary angles vertical angles Angle bisector Vocabulary

Vertical angles are two nonadjacent angles formed by two intersecting lines.  1 and  3 are vertical angles, as are  2 and  4.

An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK  KJM.

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. Example 1: Identifying Angle Pairs  AEB and  BED  AEB and  BED have a common vertex, E, a common side, EB, and no common interior points. Their noncommon sides, EA and ED, are opposite rays. Therefore,  AEB and  BED are adjacent angles and form a linear pair.

Check It Out! Example 2  5 and  6 Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.  5 and  6 are adjacent angles. Their noncommon sides, EA and ED, are opposite rays, so  5 and  6 also form a linear pair.

Find the measure of each of the following. Example 3: Finding the Measures of Complements and Supplements A. complement of  F B. supplement of  G 90  – 59  = 31  (180 – x)  180 – (7x+10)  = 180  – 7x – 10 = (170 – 7x)  (90 – x) 

Example 4: Finding the Measure of an Angle Copy the image and label it!!! KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

Example 4 Solution Step 1 Find x. mJKM = mMKL (4x + 6)° = (7x – 12)° +12 4x + 18 = 7x –4x 18 = 3x 6 = x Def. of  bisector Substitute the given values. Add 12 to both sides. Simplify. Subtract 4x from both sides. Divide both sides by 3. Simplify. Step 2 Find mJKM. mJKM = 4x + 6 = 4(6) + 6 = 30 Substitute 6 for x. Simplify.

Example 5: Identifying Vertical Angles Name the pairs of vertical angles.  HML and  JMK are vertical angles.  HMJ and  LMK are vertical angles. Check m  HML  m  JMK  60°. m  HMJ  m  LMK  120°.

Do Now Can you pass this quiz? mXYZ = 2x° and mPQR = (8x - 20)°. 1. If XYZ and PQR are supplementary, find the measure of each angle. 2. If XYZ and PQR are complementary, find the measure of each angle. 22°; 68° 40°; 140°

Assignment #4 pg 38#7-37odds 42-45, 47

Do Now – look at internet for learning target and complete do now in your new notebook 1. YV bisects XYZ and mXYV is 8x + 10 and mZYV is 12x – 6. Draw a picture, label the picture and find the value of x. 2. mXYZ = 2x° and mPQR = (8x - 20)°. If XYZ and PQR are complementary, find the measure of each angle. 22°; 68° x = 4

What if...? Suppose m  3 = 27.6°. Find m  1, m  2, and m  4. Check It Out! Example 4

2 Make a Plan If  1   2, then m  1 = m  2. If  3 and  1 are complementary, then m  1 = (90 – 27.6)°. If  4 and  2 are complementary, then m  4 = (90 – 27.6)°.

1 Understand the Problem The answers are the measures of  1,  2, and  4. List the important information:  1   2  1 and  3 are complementary, and  2 and  4 are complementary. m  3 = 27.6°

Solve 3 By the Transitive Property of Equality, if m  1 = 62.4° and m  1 = m  2, then m  2 = 62.4°. Since  3 and  1 are complementary, m  3 = 27.6°. Similarly, since  2 and  4 are complementary, m  4 = 27.6°.

Look Back4 The answer makes sense because 27.6° ° = 90°, so  1 and  3 are complementary, and  2 and  4 are complementary. Thus m  1 = m  2 = 62.4°; m  4 = 27.6°.