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Example 3-4b Objective Identify and apply angle relationships

Example 3-4b Vocabulary Vertical angles Opposite angles formed by the intersection of two lines 1

Example 3-4b Vocabulary Congruent angles Angles that have the same measure

Example 3-4b Vocabulary Supplementary angles Two angles that have the sum of their measures as 180 0

Example 3-4b Vocabulary Complementary angles Two angles are complementary if the sum of their measures is 90 0

Example 3-4b Math Symbols Is congruent to 

Lesson 3 Contents Example 1Classify Angles Example 2Classify Angles Example 3Find a Missing Angle Measure Example 4Use Angles to Solve A Problem

Example 3-1a Classify the pair of angles as complementary, supplementary, or neither Answer:. Add the two angle measurements together Supplementary 1/ Meets the definition of supplementary angles

Example 3-1b Answer: complementary Classify the pair of angles as complementary, supplementary, or neither 1/4

Example 3-2a Classify the pair of angles as complementary, supplementary, or neither  x and  y form a right angle Complementary Right angle = /4 Meets the definition of complementary angles Answer:

Example 3-2b Answer: supplementary Classify the pair of angles as complementary, supplementary, or neither 2/4

Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS  PQS and  RQS are supplementary Remember: Supplementary angles = /4 m  PQS is 56 0 m  PQS + m  RQS = 180 0

Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS /4 Replace m  PQS with 56 0 m  PQS + m  RQS = Bring down + m  RQS = m  RQS = Solve for the unknown m  RQS

Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS. 3/4 Ask “what is being done to the variable?” m  PQS + m  RQS = m  RQS = The variable (m  RQS) is being added by 56 0 Do the inverse on both sides of the equal sign Bring down Subtract

Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS. 3/4 m  PQS + m  RQS = m  RQS = Bring down + m  RQS = Subtract m  RQS = Combine “like” terms 0 Bring down + m  RQS = Combine “like” terms + m  RQS = 124 0

Example 3-3a Angles PQS and RQS are supplementary. If m  PQS 56 , find m  RQS. 3/4 m  PQS + m  RQS = m  RQS = Use the Identify Property to add m  RQS m  RQS = m  RQS = m  RQS = Answer: Bring down 124 0

Example 3-3b Angles MNP and KNP are complementary. If m  MNP 23 , find m  KNP. Answer: m  KNP = 67  3/4

Example 3-4a GEOMETRY The rectangle shown is divided by a diagonal. Find the value of x. The angle that x 0 and 70 0 make is a right angle 4/4 A right angle = 90 0 Write an equation x = 90 0 Solve for the unknown

Example 3-4a GEOMETRY The rectangle shown is divided by a diagonal. Find the value of x. 4/4 x = 90 0 Ask “what is being done to the variable?” The variable is being added by 70 0 Do the inverse on both sides of the equal sign Bring down x X Subtract

Example 3-4a GEOMETRY The rectangle shown is divided by a diagonal. Find the value of x. 4/4 x = 90 0 Bring down = 90 0 x Subtract = Combine “like” terms Bring down x 0 + x 0 +0 Bring down = = Combine “like” terms 20 0 Use the Identify Property to add x x0x0 = 20 0 Answer: Bring down 20 0

Example 3-4b GRAPHING In the circle graph shown below, find the value of x. Answer: x = 62 0 * 4/4

End of Lesson 3 Assignment Lesson 10:3Angle Relationship All