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mariarad [96]
3 years ago
8

If the ratio of a circle's sector to its total area is 1/3, what is the measure of

Mathematics
1 answer:
nalin [4]3 years ago
4 0

Answer:

option A:  120°

Step-by-step explanation:

Area \ of \ circle = \pi r^2\\\\Area \ of \ sector = \pi r^2 \frac{ \theta}{360}\\\\Ratio \ of \ sector \ to \ circle = \frac{1}{3}\\\\That is, \\\frac{1}{3} = \frac{\pi r^2 \frac{\theta}{360}} {\pi r^2}\\\\\\\frac{1}{3} = \frac{\theta}{360} \\\\\frac{360}{3} = \theta\\\\120 = \theta

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<img src="https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Ctext%7BQuestion%7D%7D%7D%20%3A%20" id="TexFormula1"
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Answer:

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

1)\text{ } AD\text{ bisects } \angle BAC                                  Given

2)\text{ } \angle BAD \cong \angle CAD                                    Definition of Bisector

\displaystyle 3) \text{ } A D \parallel E C                                               Given

\displaystyle 4)\text{ } \angle CAD\cong \angle ACE                                    Alternate Interior Angles Theorem*

\displaystyle 5) \text{ } \angle BAD\cong \angle BEC                                   Corresponding Angles Theorem*

6)\text{ } \angle CAD\cong \angle BEC                                   Substitution

7)\text{ } \angle ACE\cong\angle BEC                                    Substitution

\displaystyle 8)\text{ } AC = A E                                              Isosceles Theorem Converse

*Please refer to the attachment below.

Let me know if you have any questions!

3 0
3 years ago
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