Question

Given that ABCD is a rhombus, what is the value of x? (4x-25)

Answer 1

x + 4x - 25 = 90
5x -25 = 90
5x = 115
x = 23

answer B. 23

Answer 2

The value of x is 23°

Solution-

Given,

`m\angle CAD=2x^(\circ)\\\\m\angle CBD=(4x-25)^(\circ)`

As ABCD is a rhombus, the diagonals bisect the vertex angles of a rhombus .

So,

`m\angle A=2* m\angle CAD=2x^(\circ)\\\\m\angle B=2* m\angle CBD=2(4x-25)^(\circ)`

As in a rhombus, the consecutive angles are complementary,

`\Rightarrow m\angle A+m\angle B=180^(\circ)`

`\Rightarrow 2x+2(4x-25)=180^(\circ)`

`\Rightarrow 2x+8x-50^(\circ)=180^(\circ)`

`\Rightarrow 10x=180^(\circ)+50^(\circ)=230^(\circ)`

`\Rightarrow x=23^(\circ)`