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

Answer-

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,

$m\angle A=2\times m\angle CAD=2x^{\circ}\\\\m\angle B=2\times m\angle CBD=2(4x-25)^{\circ}$

As in a rhombus, the consecutive angles are complementary,

$\Rightarrow m\angle A+m\angle B=180^{\circ}$

$\Rightarrow 2x+2(4x-25)=180^{\circ}$

$\Rightarrow 2x+8x-50^{\circ}=180^{\circ}$

$\Rightarrow 10x=180^{\circ}+50^{\circ}=230^{\circ}$

$\Rightarrow x=23^{\circ}$