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The angles of a quadrilateral are $x$, $5x + 15^\circ $, $3x - 25^\circ$, and $4x - 20^\circ $. Find the measure of the largest angle of the quadrilateral.

eileenthecoolbean  Aug 7, 2017

Best Answer 

 #1
avatar+7177 
+3

The sum of the angles in a quadrilateral  =  360°     So.....

 

x   +   5x + 15   +   3x - 25   +   4x - 20     =  360

                                                                                 Combine like terms.

13x - 30  =  360

                                                     Add  30  to both sides of the equation.

13x  =  390

                                                     Divide both sides of the equation by  13  .

x  =  30

 

Since  x  is positive, the largest angle must be  5x + 15 .

( It has the largest coefficient of  x  and all the others either add nothing or subtract something. )

 

And..... if  x  =  30,       5x + 15  =  5(30) + 15  =  165°

hectictar  Aug 7, 2017
 #1
avatar+7177 
+3
Best Answer

The sum of the angles in a quadrilateral  =  360°     So.....

 

x   +   5x + 15   +   3x - 25   +   4x - 20     =  360

                                                                                 Combine like terms.

13x - 30  =  360

                                                     Add  30  to both sides of the equation.

13x  =  390

                                                     Divide both sides of the equation by  13  .

x  =  30

 

Since  x  is positive, the largest angle must be  5x + 15 .

( It has the largest coefficient of  x  and all the others either add nothing or subtract something. )

 

And..... if  x  =  30,       5x + 15  =  5(30) + 15  =  165°

hectictar  Aug 7, 2017

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