Pre-AP Bellwork

1
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?

2
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.

3
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.

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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.

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1-5 Exploring Angle Pairs
6

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

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Which angles are adjacent?
? 1 ? 2, ? 2 ? 3, ? 3 ? 4, ? 4 ? 1
Then what do we call ? 1 ? 3?
Vertical Angles 2 angles that share a common
vertex whose sides form 2 pairs of opposite
rays. ? 1 ? 3, ? 2 ? 4
2
1 3
4
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Linear Pair (of angles)

• 2 adjacent angles whose non-common sides are
  opposite rays.

1 2
9
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 ? 4

2
1 3
5 4
10
Important Facts

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

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Example

• If m ? 5130o, find
• m ? 3
• m ? 6
• m ? 4

4
130o 50o 50o
5 3
6
12
Example
A
E
3x5o y20o

• Find x,y
• m ? ABE
• m ? ABD
• m ? DBC
• m ? EBC

B
x15o 4y-15o
D
C
x40 y35 m?ABE125o m ? ABD55o m ? DBC125o m ?
EBC55o
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Complementary Angles

• 2 angles whose sum is 90o

35o
1
2
55o
A
? 1 ? 2 are complementary ? A ? B are
complementary
B
14
Supplementary Angles

• 2 angles whose sum is 180o

? 1 ? 2 are supplementary. ? X ? Y are
supplementary.
1 2
130o 50o
X Y
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Ex ? A ? B are supplementary. m ? A is 5 times
m ? B. Find m ? A m ? B.

• m ? A m ? B 180o
• m ? A 5(m ? B)
• Now substitute!
• 5(m ? B) m ? B 180o
• 6(m ? B)180o
• m ? B30o
• m ? A150o