Question

The figure shown is a rhombus.

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

A. x + y = z
B. 2x = y + z
C. z + x = 2y
D. 2x + 2y = 4z

Answer 1

Answer: The equation that is true regarding the angles formed by the diagonals and sides of the rhombus is the indicated in option A. x+y=z

Solution:

In a rhombus the diagonals are perpendicular, then the angle z° must be equal to 90° (z=90)

In any triangle, the sum of the interior angles must be equal to 180°, then according with the figure:

x°+y°+z°=180°

(x+y+z)°=180°

x+y+z=180

Like z=90

x+y+90=180

Subtracting 90 both sides of the equation:

x+y+90-90=180-90

x+y=90

Then:

x+y=90

z=90

90=90→x+y=

Answer: Option A. x+y=z

Answer 2

Ans: A
Since x + y + z = 180° and z = 90°, y + z = 90°
Thus x + y = z