Answer :

chibabykalu16

Answer:

36 degrees

Step-by-step explanation:

To find the angle measure of an arc bounding a sector with an area of 10π square inches in a circle with a radius of 10 inches, we can use the formula for the Area of a sector of a circle:

[tex]\text{Area of sector} = \frac{\theta}{360} \cdot \pi r^2[/tex]

where:

  • θ is the angle in degrees. (also known as theta)
  • r is the radius of the circle.
  • π is approximately 3.14159.

Given:

  • The area is 10π square inches
  • r is 10 inches

Substituting the known values into the formula:

[tex]10\pi = \frac{\theta}{360} \cdot \pi \cdot 10^2[/tex]

[tex]10\pi = \frac{\theta}{360} \cdot 100\pi[/tex]

Divide both sides by π:

[tex]10 = \frac{\theta}{360} \cdot 100[/tex]

Solving for :

[tex]10 = \frac{100\theta}{360}[/tex]

[tex]10 = \frac{5\theta}{18}[/tex]

Multiply both sides by 18:

[tex]180 = 5\theta[/tex]

Divide both sides by 5:

[tex]\theta = 36^\circ[/tex]

Therefore, the angle measure of the arc bounding the sector is 36°.

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