Question

Find the value of xx, yy, and zz in the rhombus below.
108°
(-x+1)°
(-2y+4)°
(3z+9)°

Answer 1

In a rhombus opposite angles are equal and adjacent angles are supplementary. The angles are given in order, so angle 1 (108°) is opposite angle 3 (-2y+4)°, and angles 2 (-x+1)° and 4 (3z+9)° are opposite.

1) -2y + 4 = 108
-2y = 104
y = -52

2) 108 + (-x + 1) = 180 (adjacent angles sum to 180)
-x + 1 = 72
x = -71

3) The opposite of angle 2 is angle 4, so 3z + 9 = -x + 1 = 72
3z = 63
z = 21

Answer: x = -71, y = -52, z = 21. (Check: the four angles are 108°, 72°, 108°, 72°.)