Question

Find the values of x, y, and z in the triangle to the right

Answer 1

Answer:

x = 36 , y = 64 , z = 80

Step-by-step explanation:

Exterior angle equals the sum of opposite interior angle.

3x +  8 = x +  z

3x - x - z = -8

2x  -  z = -8   ------------ (I)

z + 3x - 8 = 180 {linear pair}

3x + z = 180 + 8

3x + z = 188 --------------(II)

Add (I) and (II) and z will be eliminated and we can find the value of 'x'

(I)            2x - z = -8

(II)           3x + z = 188   {Now add}

               5x      = 180

x = 180/5

x = 36

Plugin x = 36 in equation (II)

     3*36 +z = 188

        108 + z = 188

                z = 188- 108

z = 80

x + y + z = 180 ----------------(III)  {angle sum property of triangle}

36 + 80 +y = 180

       116 + y = 180

               y = 180 - 116

y = 64