Answer:
The length of [tex]\overline{JO}[/tex] is 48.
Step-by-step explanation:
A square is a quadrilateral whose four sides have the same length and four internal angles have the same measure. The sum of measures of internal angles in quadrilaterals equals 360°. Let [tex]m\,\angle BOJ = 4\cdot x -6[/tex] and [tex]BO = 2\cdot x - 8[/tex], the value of [tex]x[/tex] is:
[tex]4\cdot (4\cdot x - 6) = 360^{\circ}[/tex]
[tex]16\cdot x -24 = 360^{\circ}[/tex]
[tex]16\cdot x = 384^{\circ}[/tex]
[tex]x = 24[/tex]
And the length of [tex]JO[/tex] is:
[tex]JO = BO = 2\cdot x - 8[/tex]
[tex]JO = 40[/tex]
The length of [tex]\overline{JO}[/tex] is 48.
