Answer:
The value of [tex]x[/tex] is 10.
Step-by-step explanation:
If APR and SPL are vertical angles, then we get that [tex]\angle APR = \angle SPL[/tex]. Given that [tex]\angle APR = 13\cdot x -30[/tex] and [tex]\angle SPL = 3\cdot x + 70[/tex], we find that the value of [tex]x[/tex] is:
[tex]13\cdot x - 30 = 3\cdot x +70[/tex]
[tex]10\cdot x = 100[/tex]
[tex]x = 10[/tex]
The value of [tex]x[/tex] is 10.
