22. in the diagram below wxz is a right angle. if the measure of wxv is 11 more than there times the measure of wxy and the measure of yxv = 139, find the measure of yxz

Given: < WXZ = 90 degrees ( Right angle is an angle of 90 degree measure).

      m< WXV = 11 more than 3 times m< WXY = (3 * <WXY + 11)

      m< YXV = 139 degree.

To find : m<YXZ = ?

Solution : m< WXZ is equal to 90 degrees and is  also the sum of angles m<WXY and m<YXZ i.e.

          m< WXZ = 90 degrees = m<WXY + m<YXZ            (1)

           m< WXV = (3 * <WXY + 11)                       (2)

          m <YXV is equal to 139 degrees and also equal to the sum of angles m<WXY and m<WXV i.e.

          m <YXV = 139 degree = m<WXY + m<WXV            (3)

Substituting m< WXV = (3 * <WXY + 11) from equation (2) in equation (3)

         139 degree = m<WXY + m<WXV

      => 139 = m<WXY + 3 * m<WXY + 11  (Subtracting 11 from both sides)

      => 139 -11 =  m<WXY + 3 * m<WXY + 11 -11            

      => 128 = 4<WXY                                      (Adding m<WXY + 3 * m<WXY)

      => 32  = < WXY                                      (Dividing both sides by 4)

Substituting  < WXY = 32 from above in equation (1)

      90 degrees = m<WXY + m<YXZ

      90 = 32 + m<YXZ                                (Subtracting 32 from both sides)                                  

      90-32 = 32 + m<YXZ -32

      58 = m<YXZ.

Therefore, <YXZ =58 degrees.

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