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3 years ago

Circles and angles: find f

Mathematics

1 answer:

Irina-Kira [14]3 years ago

5 0

Answer:

130°

Step-by-step explanation:

$e = \frac{1}{2} (100 \degree - 80 \degree) \\ \\ e = \frac{1}{2} \times 20 \degree \\ \\ e = 10 \degree \\ \\ a = \frac{1}{2} \times 80 \degree \\ \\ a = 40 \degree \\ \\ by \: interior \: \angle \: sum \: postulate \: of \: a \: \triangle \\ a + e + f = 180\degree \\40\degree + 10\degree + f = 180\degree \\50\degree + f = 180\degree \\f = 180\degree - 50\degree \\\huge \red {\boxed {f = 130\degree}}$

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3 years ago

The sector COB is cut from the circle with center O. The ratio of the area of the sector removed from the whole circle to the ar

mafiozo [28]

Answer:

$Ratio = \frac{R^2 - r^2 }{ r^2}$

Step-by-step explanation:

Given

See attachment for circles

Required

Ratio of the outer sector to inner sector

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$Area = \frac{\theta}{360}\pi r^2$

For the inner circle

$r \to radius$

The sector of the inner circle has the following area

$A_1 = \frac{\theta}{360}\pi r^2$

For the whole circle

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The sector of the outer sector has the following area

$A_2 = \frac{\theta}{360}\pi (R^2 - r^2)$

So, the ratio of the outer sector to the inner sector is:

$Ratio = A_2 : A_1$

$Ratio = \frac{\theta}{360}\pi (R^2 - r^2) : \frac{\theta}{360}\pi r^2$

Cancel out common factor

$Ratio = R^2 - r^2 : r^2$

Express as fraction

$Ratio = \frac{R^2 - r^2 }{ r^2}$

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3 years ago

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Answer:
$300

Explanation:
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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago