Answer:
4. θ = 139.80°
5. x = 9
Step-by-step explanation:
4.
From the picture you can see that the radius is 10 in and the arc length is 24.4 in.
Since you got radius and arc length you can use arc length formula to get the angle!
Formula for arc length is:
[tex]\text{arc length} = 2 \pi r (\frac{\theta}{360^\circ})[/tex]
where r is radius and θ is the angle in degree.
Substituting the values:
[tex]24.4 = 2 \cdot \pi \cdot 10 \cdot (\frac{\theta}{360^\circ})[/tex]
Now let's rearrange the equation to isolate θ.
[tex]24.4 = 2 \cdot \pi \cdot 10 \cdot (\frac{\theta}{360}) \\\\24.4 = 20 \cdot \pi \cdot (\frac{\theta}{360})\\\\\frac{24.4}{20 \pi} = \frac{\theta}{360}\\\\\frac{24.4 \cdot 360}{20 \pi} = \theta\\\\\frac{24.4 \cdot 360}{20 \pi} = \theta\\\\\frac{8784}{20 \pi} = \theta\\\\139.8017^\circ \approx \theta\\\\\text{Rounding to 2 decimal places:}\\\theta = 139.80^\circ[/tex]
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5.
For this one let's use the Two Tangent Theorem, which states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.
Therefore:
x + 6 = 3x - 12
18 = 2x
9 = x
