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4 years ago

Find the measure of a central angle of a regular polygon with 10 sides

Mathematics

1 answer:

Paraphin [41]4 years ago

5 0

Answer:

114 degrees

Step-by-step explanation:

The formula to find the measure of all angles in a regular polygon is $(n-2)180$ , where n = total number of sides.

Thus, we substitute n for 10, and you get:

$(10-2)180=1440$

If the shape is a regular polygon and it has ten sides, meaning all sides are equal, then all you do is divide 1440 by 10, to get the final answer of 114.

A central angle in a regular ten-sided polygon would be 144 degrees.

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Graph the image of this figure after a dilation with a scale factor of 13 centered at the point (4, −2) .

Sonja [21]

Answer:

From the given triangle figure;

Labelled the triangle as A , B and C.

The coordinates of this triangle ABC are;

A = (1, 10) ,

B = (-2, 4)

C = (7, 4).

Given : Scale factor(k) = $\frac{1}{3}$ and centered at point (4, -2).

The rule of dilation with $k= \frac{1}{3}$ and center at point (4,-2) is:

$(x, y) \rightarrow (\frac{1}{3}(x-4)+4 , \frac{1}{3}(y+2)-2)$

$(x, y) \rightarrow (\frac{1}{3}x-\frac{4}{3}+4 , \frac{1}{3}y+\frac{2}{3}-2)$

$(x, y) \rightarrow (\frac{1}{3}x+\frac{8}{3} , \frac{1}{3}y-\frac{4}{3})$

then, the dilation of the given figure are;

$A(1, 10) \rightarrow (\frac{1}{3}\cdot 1+\frac{8}{3} , \frac{1}{3} \cdot 10-\frac{4}{3})$ = $(\frac{1}{3}+\frac{8}{3} , \frac{10}{3}-\frac{4}{3})$ = $(\frac{9}{3} , \frac{6}{3})$ = A'(3 , 2)

$B(-2, 4) \rightarrow (\frac{1}{3}\cdot -2+\frac{8}{3} , \frac{1}{3} \cdot 4-\frac{4}{3})$ = $(-\frac{2}{3}+\frac{8}{3} , \frac{4}{3}-\frac{4}{3})$ = $(\frac{6}{3} , \frac{0}{3})$ =B'(2 , 0)

$C(7, 4) \rightarrow (\frac{1}{3}\cdot 7+\frac{8}{3} , \frac{1}{3} \cdot 4-\frac{4}{3})$ = $(\frac{7}{3}+\frac{8}{3} , \frac{4}{3}-\frac{4}{3})$ = $(\frac{15}{3} , \frac{0}{3})$ = C'(5 , 0)

The coordinates of dilation images are:

A' = (3,2) , B' = (2, 0) and C' = (5, 0)

You can see the graph of the dilated image as shown below:

3 0

3 years ago

Read 2 more answers

WHAT IS THE MEASURE OF ANGLE T NEED HELP

MissTica

Because the lines are parallel two x angles are 27 and angles in a triangle = 180 so double 27 to get 54, then 180-54= 126 so t should be 126 degrees, but if not sorry

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3 years ago

Gerald buys a bag of 7500 assorted beads online a random sample of 150 beads contains 17 red beads. Predict the number of assort

Deffense [45]

Answer:

850 red beads

Step-by-step explanation:

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red beads/red beads = total beads/total beads

Let x = the no. of red beads in the bag

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x = 17(7500)/150 = 850 red beads

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3 years ago

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Answer:

Step-by-step explanation:

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siniylev [52]

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Step-by-step explanation:

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