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The figure shows two intersecting lines.  What is the value of x?

 

 Sep 16, 2020
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Since vertical angles are congruent, we can make the following equation:

 

(4x + 7)°   =   (7x - 35)°

                                           We can remove the degree signs and parenthesees from both sides of the equation.

4x + 7   =   7x - 35

                                           Subtract 4x from both sides, add  35  to both sides.

7 + 35   =   7x - 4x

                                           Combine like terms.

42   =   3x

                                           Divide both sides of the equation by  3

?   =   x

 

 

 

 

Alternate approach:

 

Since a  180°  angle forms a straight line, we can make the following equation:

 

(4x + 7)°  +  (10x - 23)°   =   180°

                                                       Remove the degree signs from every term, then we can drop the two

                                                       sets of parenthesees because there is only addition between them

4x + 7  +  10x - 23   =   180

                                                       Simplify the left side by combining like terms.

14x  -  16   =   180

                                                       Add  16  to both sides.

14x   =   196

                                                       Divide both sides of the equation by  14

x   =   ?

 Sep 16, 2020

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