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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.

Aug 7, 2017

#1
+7347
+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°

Aug 7, 2017

#1
+7347
+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