Answer:
x = [tex]10^{o}[/tex]
Step-by-step explanation:
The diagonals of a rhombus are perpendicular to each other, thus the angle at point E is [tex]90^{o}[/tex]. So that ΔCED is a right triangle, and that;
<CDB = <CDE
<ACD = <ECD
<CDE + <ACD + <CED = [tex]180^{o}[/tex] (sum of angles in a triangle)
6x + (2x + 10) + [tex]90^{o}[/tex] = [tex]180^{o}[/tex]
8x + 100 = [tex]180^{o}[/tex]
8x = [tex]180^{o}[/tex] - 100
8x = 80
x = [tex]\frac{80}{8}[/tex]
= [tex]10^{o}[/tex]
Thus, the value of x is [tex]10^{o}[/tex].
