X = measure of angle 1 y = measure of angle 2 z = measure of angle 3 w = measure of angle 4
Focus on the bottom triangle. The three angles add to 180 degrees (angle 2) + (angle 3) + 116 = 180 y+z+116 = 180 y+z= 180-116 y+z= 64
Since we have the bottom triangle as isosceles, this means that y = z, so y+z = 64 y+y = 64 2y = 64 y = 64/2 y = 32 making z = 32 as well
Similarly, angle 1 and angle 4 are 32 degrees because the 116 angle is opposite the top left-most angle, and congruent to this angle. In other words, the bottom triangle is a mirror image of the top triangle.
The figure is a rhombus because all four sides are the same length (as shown by the tickmarks)
