Question

Given that ABCD is a rhombus, what is the value of x?

answers
a.) 28
b.) 56
c.) 48.5
d.) 18
e.) 36
f.) Cannot be determined

Answer 1

d

Explanation:

We know that diagonals bisect angles of a rhombus, meaning that they split the angles of two equal parts, that opposite angles are equal, and that the angles of a quadrilateral, such as a rhombus, add up to 360 degrees.

Looking at the drawing I uploaded, and taking into account that diagonals bisect angles of a rhombus, we can say that angle x = y and z = 5x-18

Next, given that opposite angles are equal, we can say that angle B = angle D and angle A = angle C. Therefore,

A+B+C+D= 360 (as the angles of a quadrilateral add up to 360)

A + B + A + B = 360 (plugging in A for C and B for D)

2 ( A + B) = 360

A + B = 180

x + y + z + 5x - 18 = 180 (plugging x+y in for A, and z+5x-18 in for B, as x and y make up A and z and 5x-18 make up B)

x+x+5x-18+5x-18 = 180 (because x=y and z=5x-18)

2(x+5x-18) = 180

divide both sides by 2

x+5x-18=90

6x-18=90

add 18 to both sides

6x=108

divide both sides by 6

x = 18