Question

If angle 1 and angle 7 are vertical angles and angle 1 and angle 2 are supplementary adjacent and the measure of angle 2 is 123 degrees. what is the measure of angle 7?

Answer 1

Answer:  m∡7 = 57° .
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Explanation:
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 m∡7 = m∡1 ;  SInce  these angles are vertical; and vertical angles are congruent.

m∡1 + m∡2 = 180 ; since these angles are supplementary; and by                                            definition; supplementary angles "add up" to 180.

Given: m∡2 = 123 ;  

m∡1 + 123 = 180 ;

Since m∡1 = m∡7 ; and we wish to find: "m∡7" ;  we can rewrite as:
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m∡7 + 123 = 180 ; solve for "m∡7" ;
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Subtract "123" from EACH SIDE of the equation:
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  m∡7 + 123 - 123 = 180 - 123 ;
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  m∡7 = 57° .
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