The value of x is 1.
Step - by - Step Explanation
What to find? The value of x.
Given:
From the diagram,
• Inscribed angle = 70°
,
• arc length = 141x - 1
The formula we can use to solve the given problem is;
[tex]\text{Inscribed angle =}\frac{1}{2}(\text{ length of arc)}[/tex]
Substitute the values into the formula.
[tex]70=\frac{1}{2}(141x\text{ - 1)}[/tex]
Simplify the above.
To simplify, first multiply both-side of the equation by 2.
[tex]70\times2=\cancel{2}\times\frac{1}{\cancel{2}}(141x-1)[/tex]
140 = 141x - 1
Add 1 to both-side of the equation.
140 + 1 = 141x -1 + 1
141 = 141x
Divide both-side of the equation by 141.
[tex]\frac{\cancel{141}x}{\cancel{141}}=\frac{141}{141}[/tex]
x = 1
