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 #1
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Draw WY to create △WXY .

 

△WXY is an isoscelese right triangle so the measure of each base angle is  45°

 

The length of each leg of  △WXY  is  4  so the length of the hypotenuse is  4√2

 

 

 

m∠XYZ  =  135°

 

m∠WYZ  =  m∠XYZ - m∠WYX  =  135° - 45º  =  90°

 

So  △WYZ  is a right triangle, and we know the length of two of the sides.

To find the length of the missing side, we can use the Pythagorean theorem.

 

a2  +  ( 4√2 )2   =   92

 

a2  +  32   =   81

                                Subtract  32  from both sides.

a2   =  49

                                Take the positive sqrt of both sides.

a  =  7

 May 30, 2019
 #2
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+1

Thank you!!!

 May 30, 2019

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