Lesson 2-4 Special Pairs of Angles (page 50) Essential Question Can you justify the conclusion of a conditional statement?

Complementary Angles: … two angles whose measures have the sum 90 degrees. Example: A C B 60º 30º

Supplementary Angles: … two angles whose measures have the sum 180 degrees. Example: 1 2

Example #1. In the diagram, ∠ CXD is a right angle. A B C E Name another right angle. _________________________________ X D

Example #1. In the diagram, ∠ CXD is a right angle. A B C E Name complementary angles. _________________________________ X D

Example #1. In the diagram, ∠ CXD is a right angle. A C E Name 2 congruent supplementary angles. _________________________________ X D B

Example #1. In the diagram, ∠ CXD is a right angle. A C E Name 2 noncongruent supplementary angles. ________________________________________________ X D B

Example # 2. ∠ C and ∠ D are complementary, m ∠ C = 3x - 5 and m ∠ D = x Find the value of x, m ∠ C, and m ∠ D. x = ______ m ∠ C = _____ m ∠ D = _____ = 90º

Example # 3. ∠ P and ∠ K are supplementary, m ∠ P = 4x + 10 and m ∠ K = x Find the value of x, m ∠ P, and m ∠ K. x = ______ m ∠ P = _____ m ∠ K = _____ = 180º

Example #4.A supplement of an angle is seven times a complement of the angle. Find the measures of the angle, its complement, and its supplement. measure of angle = __________ = ________ measure of complement = __________ = ________ measure of supplement = __________ = ________

Example #5.A complement of an angle is 15 less than twice the measure of the angle. Find the measures of the angle, its complement, and its supplement. measure of angle = __________ = ________ measure of complement = __________ = ________ measure of supplement = __________ = ________

Vertical Angles: … two angles whose sides form two pairs of opposite rays. Example: _______________and _______________

Vertical angles are congruent. Theorem 2-3 Vert. ∠ ’s R ≅ Given: ∠ 1 and ∠ 2 are vertical angles Prove: ∠ 1 ≅ ∠

StatementsReasons 1.______________________________________ 2.______________________________________ ___________________ 3.___________________ ___________________ 4.______________________ ___________________ 5.___________________ ___________________ 6.___________________ ___________________ Given Angle Add. Post. m ∠ 1 = m ∠ 2 ∠ 1 ≅ ∠ 2 ∠ 1 and ∠ 2 are vertical angles m ∠ 1 + m ∠ 3 = 180º m ∠ 1 + m ∠ 3 = m ∠ 2 + m ∠ 3 Substitution Prop. m ∠ 3 = m ∠ 3 Reflexive Prop. Subtraction Prop. Def. of ≅ ∠ ’s Given: ∠ 1 and ∠ 2 are vertical angles Prove: ∠ 1 ≅ ∠ m ∠ 2 + m ∠ 3 = 180º

Example #4. Find the value of “x”. 35º(2x-5)º x = _______ 20

Example #5. Find the value of “x”. 35º xº x = _______ 55 xº

Example #6. Find the value of “x”. (x+30)º4xº x = _______ 10

Example #7. Find the values of “x” and “y”. (2x+30)º 4yº x = _______ y = _______ (x+y)º 120º 45 15

Example #8. Find the measure of each angle. 60º B C A E D G F 60º 90º 90º-60º = 30º 30º

Assignment Written Exercises on pages 52 to 54 RECOMMENDED: 1 to 17 odd numbers REQUIRED: 19 to 31 odd numbers, 32 to 35 Assignment Worksheet on Lesson 2-4 Prepare for a Quiz on Lesson 2-4: Special Pairs of Angles Can you justify the conclusion of a conditional statement?