Given:
A figure.
[tex]m \angle C D A=9 x+3[/tex] and [tex]m \angle E D A=6 x+5[/tex]
To find:
What kind of figure and the value of x
Solution:
All four sides are congruent.
Diagonals bisect each other.
There the given figure is rhombus.
Diagonals bisect the angles.
⇒ [tex]m \angle C D A=m \angle E D A[/tex]
[tex]9 x+3=6x+5[/tex]
Subtract 3 on both sides.
[tex]9 x+3-3=6x+5-3[/tex]
[tex]9 x=6x+2[/tex]
Subtract 6x from both sides.
[tex]9 x-6x=6x+2-6x[/tex]
[tex]3x=2[/tex]
Divide by 3 on both sides.
[tex]$\frac{3x}{3} =\frac{2}{3} $[/tex]
[tex]$x=\frac{2}{3} $[/tex]
The value of x is [tex]\frac{2}{3}[/tex].
