Answer:
x=6
Step-by-step explanation:
So we have the difference of the intercept arcs divided by 2 is the angle formed by the two tangents there.
So we have
[tex]\frac{(37x+5)-(23x-5)}{2}=5x+17[/tex]
Clear the fraction by multiplying both sides by 2:
[tex](37x+5)-(23x-5)=2(5x+17)[/tex]
Distribute:
[tex]37x+5-23x+5=10x+34[/tex]
Combine like terms on the left hand side:
[tex]37x-23x+5+5=10x+34[/tex]
Simplify:
[tex]14x+10=10x+34[/tex]
Subtract 10x on both sides:
[tex]4x+10=34[/tex]
Subtract 10 on both sides:
[tex]4x=24[/tex]
Divide both sides by 4:
[tex]x=6[/tex]
