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2 years ago

Each interior angle of a regular polygon has a measure of 40.how many sides does the polygon have?

Mathematics

1 answer:

zysi [14]2 years ago

5 0

Given Information :-

⠀

Each exterior angle of a regular polygon has a measure of 40°

⠀

To Find :-

⠀

The number of sides of the polygon

⠀

Formula Used :-

⠀

$\qquad \star \: \underline{ \boxed{ \green{ \sf No.~of~sides = \dfrac{360^ \circ}{exterior ~angle}}}} \: \star$

⠀

Solution :-

⠀

Using the formula,

⠀

$\sf \dashrightarrow No. ~of~sides= \dfrac{360}{40} \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \frac{ \cancel{360}}{ \cancel{40} } \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \underline{ \boxed{ \blue { \frak{9}}}} \: \star$

⠀

Thus, the polygon is a nonagon, and hence has 9 sides.

⠀

$\underline{\rule{227pt}{2pt}} \\ \\$

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2 years ago

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olchik [2.2K]

Option A: $\frac{1}{3}$ is the dilation factor

Explanation:

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Also, the coordinates of the square A'B'C'D' are A'(–7, 6), B'(-4,6), C'(-4,3), D'(-8,3)

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Also,

$\begin{aligned}A C &=\sqrt{(-12+21)^{2}+(9-18)^{2}} \\&=\sqrt{9^{2}+(-9)^{2}} \\&=\sqrt{81+81} \\&=\sqrt{162}\\&=9\sqrt{2} \end{aligned}$

Dividing A'C' by AC, we have,

$\frac{A'C'}{AC} =\frac{3\sqrt{2} }{9\sqrt{2}} =\frac{1}{3}$

Thus, $\frac{1}{3}$ is the dilation factor

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A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 85

insens350 [35]

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3 years ago

2^4n × 2^ 2n = 512 What is the value of n.

Marina86 [1]

Step-by-step explanation:

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