Question

In the rhombus, m<1=18x, m<2=x+y, and m<3=18z. Find the value of each variable. The diagram is not to scale.

Answer 1

Explanation:

Remark

The diagonals of a rhombus bisect each other at right angles.

Furthermore <1 and <2 are supplementary and <1 and <3 are equal so z = x (vertically opposite angles).

Formulas

Supplementary formula

x + y + 18x = 180

Right angle formula

x + y = 90

Solution

x + y + 18x = 180

x + y = 90 Subtract these two formulas

18x = 90

x = 5 Use the right angle formula to find y

x + y = 90

5 + y = 90 Subtract 5 from both sides

5-5 + y = 90-5

y = 85

Since x = z then z = 5

Answers

• x = 5
• y = 85
• z = 5