Question

The figure shown is a rhombus.

A rhombus with diagonals is shown. The diagonals form 4 triangles. The measures of the angles are x degrees, y degrees, and z degrees. All sides are congruent.

Which equation is true regarding the angles formed by the diagonals and sides of the rhombus?

x + y = z
2x = y + z
z + x = 2y
2x + 2y = 4z

Answer 1

x + y = z

Reason: In a rhombus the diagonals are perpendicular, so the angle z at their intersection is 90°. In the triangle formed by two adjacent vertices and the intersection point, x + y + z = 180°, so x + y + 90° = 180°, hence x + y = 90° = z.