Question

In the rhombus, angle 1=9x, angle 2=y+x, and angle 3=15z. Find the value of each variable. The diagram is not to scale.

A. x = 10, y = 170, z = 12
B. x = 20, y = 80, z = 12
C. x = 10, y = 80, z = 6
D. x = 20, y = 170, z = 6

Answer 1

From the diagram, all three angles are 90° (Diagonals of a Rhombus)

Angle 1 = 9x = 90
⇒ 9x = 90
x = 90/9
x = 10


Angle 2 = y + x = 90
⇒ y + x = 90
since x = 10,
y + 10 = 90
y = 90 - 10
y = 80


Angle 3 = 15 z = 90
⇒ 15z = 90
z = 90/15
z = 6

Answer is Option C
C. x = 10, y = 80, z = 6