Pre-AP Bellwork 6) Claire draws an angle that measures 56. Justin draws a congruent angle. Justin says his angle is obtuse. Is he correct? Why or why not?

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Presentation transcript:

Pre-AP Bellwork 6) Claire draws an angle that measures 56. Justin draws a congruent angle. Justin says his angle is obtuse. Is he correct? Why or why not?

Pre-AP Bellwork 7) ∠ MLN and ∠ JLK are complementary, m ∠ MLN = 7x − 1, and m ∠ JLK = 4x + 3. a. Solve for x. b. Find m ∠ MLN and m ∠ JKL. c. Show how you can check your answer.

Pre-AP Bellwork 8)Describe all the situations in which the following statements are true. a. Two vertical angles are also complementary. b. A linear pair is also supplementary. c. Two supplementary angles are also a linear pair. d. Two vertical angles are also a linear pair.

Pre-AP Bellwork Find the measure of each angle in the angle pair described. 9) The measure of one angle is 5 times the measure of its complement. 10) The measure of an angle is 30 less than twice its supplement.

1-5 Exploring Angle Pairs

Adjacent angles- two coplanar angles with a common side, a common vertex, and no common interior points

Which angles are adjacent?  1&  2,  2&  3,  3&  4,  4&  1 Vertical Angles – 2 angles that share a common vertex & whose sides form 2 pairs of opposite rays.  1&  3,  2&  4 Then what do we call  1&  3?

Linear Pair (of angles)  2 adjacent angles whose non-common sides are opposite rays. 1 2

Example  Vertical angles?  1 &  4  Adjacent angles?  1&  2,  2&  3,  3&  4,  4&  5,  5&  1  Linear pair?  5&  4,  1&  5  Adjacent angles not a linear pair?  1&  2,  2&  3,  3& 

Important Facts  Vertical Angles are congruent.  The sum of the measures of the angles in a linear pair is 180 o.

Example:  If m  5=130 o, find m  3 m  6 m  = 130 o =50 o

Example:  Find x,y m  ABE m  ABD m  DBC m  EBC 3x+5 o y+20 o x+15 o 4y-15 o x=40 y=35 m  ABE=125 o m  ABD=55 o m  DBC=125 o m  EBC=55 o A B C D E

Complementary Angles  2 angles whose sum is 90 o o A 55 o B  1 &  2 are complementary  A &  B are complementary

Supplementary Angles  2 angles whose sum is 180 o o 50 o X Y  1 &  2 are supplementary.  X &  Y are supplementary.

Ex:  A &  B are supplementary. m  A is 5 times m  B. Find m  A & m  B. m  A + m  B = 180 o m  A = 5(m  B) Now substitute! 5(m  B) + m  B = 180 o 6(m  B)=180 o m  B=30 o m  A=150 o