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ACT Math : Other Polygons

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Example Question #1 : How To Find An Angle In A Polygon

Fig_2

What is the angle measure for the largest unknown angle in the figure above? Round to the nearest hundredth.

Possible Answers:

$149.1^{\circ}$

$74.55^{\circ}$

$186.36^{\circ}$

$84.14^{\circ}$

$140.14^{\circ}$

Correct answer:

$186.36^{\circ}$

Explanation:

The total degree measure of a given figure is given by the equation 180*(s-2) , where represents the number of sides in the figure. For this figure, it is: $180*(6-2)=180*4 = 720^{\circ}$

Therefore, we know that the sum of the angles must equal $720^{\circ}$ . This gives us the equation:

$90^{\circ}+120^{\circ}+100^{\circ}+x+2.5x+2x=720^{\circ}$

Simplifying, this is:

$310^{\circ}+5.5x=720^{\circ}$

Now, just solve for :

5.5x=410

$x=\frac{410}{5.5}$

The largest of the unknown angles is 2.5x or $2.5 * \frac{410}{5.5}=186.36363636363636...^{\circ}$

Rounding, this is $186.36^{\circ}$ .

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Example Question #2 : How To Find An Angle In A Polygon

What is the interior angle of a $\textup{9-sided}$ polygon (a nonagon)? Round answer to the nearest hundredth if necessary.

Possible Answers:

$360^{\circ}$

$140^{\circ}$

$128.57^{\circ}$

$147.27^{\circ}$

$1260^{\circ}$

Correct answer:

$140^{\circ}$

Explanation:

To find the interior angle of an sided polygon, first find the total number of degrees in the polygon by the formula:
$(n-2)*180^{\circ}$ . For us that yields:
$(9-2)*180^{\circ} = 1260^{\circ}$ . Next we divide the total number of degrees by the number of sides:

$1260^{\circ}/9 = 140^{\circ}$

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Example Question #3 : How To Find An Angle In A Polygon

What is the total number of degrees in a $\textup{12-sided}$ polygon?

Possible Answers:

$1440^{\circ}$

$150^{\circ}$

$1800^{\circ}$

$144^{\circ}$

$2160^{\circ}$

Correct answer:

$1800^{\circ}$

Explanation:

To find the total number of degrees in an -sided polygon, use the formula:

(n-2)*180 thus we see that (12-2)*180 = $1800^{\circ}$

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Example Question #4 : How To Find An Angle In A Polygon

What is the interior angle of a $\textup{16-sided}$ polygon?

Possible Answers:

$2520^{\circ}$

$160^{\circ}$

$154.29^{\circ}$

$360^{\circ}$

$157.5^{\circ}$

Correct answer:

$157.5^{\circ}$

Explanation:

To find the interior angle of a regular, -sided polygon, use the formula:

((n-2)*180)/n :

Thus we see that $(16-2)*180^{\circ} = 2520^{\circ}$ and

$2520^{\circ}/16 = 157.5^{\circ}$

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Example Question #5 : How To Find An Angle In A Polygon

What is the total number of degrees in a $\textup{7-sided}$ polygon?

Possible Answers:

$1260^{\circ}$

$900^{\circ}$

$360^{\circ}$

$540^{\circ}$

$128.57^{\circ}$

Correct answer:

$900^{\circ}$

Explanation:

To find the total number of degrees in an -sided polygon, use the formula:

$(n-2)*180^{\circ}$ . Thus we see that:

$(7-2)*180 = 900^{\circ}$

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Example Question #611 : Act Math

How many degrees are in the interior of an octagon (an 8-sided polygon)?

Possible Answers:

$135^{\circ}$

$900^{\circ}$

$1440^{\circ}$

$1260^{\circ}$

$1080^{\circ}$

Correct answer:

$1080^{\circ}$

Explanation:

To find the total number of degrees in an -sided polygon, use the formula:

$(n-2)*180^{\circ}$ . Thus, for an octagon we have:

$(8-2)*180^{\circ} = 1080^{\circ}$

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Example Question #612 : Act Math

What is the interior angle of a pentagon?

Possible Answers:

$128.57^{\circ}$

$540^{\circ}$

$72^{\circ}$

$108^{\circ}$

$110^{\circ}$

Correct answer:

$108^{\circ}$

Explanation:

To find the interior angle of an -sided polygon, use the formula:

$((n-2)*180^{\circ})/n$
we see for our polygon this yields:

$((5-2)180^{\circ})/5=108^{\circ}$

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Example Question #8 : How To Find An Angle In A Polygon

What is the interior angle of a ten-sided polygon?

Possible Answers:

$180^{\circ}$

$1440^{\circ}$

$144^{\circ}$

$360^{\circ}$

$150^{\circ}$

Correct answer:

$144^{\circ}$

Explanation:

To find the interior angle of an -sided polygon, use the equation:

$((n-2)*180^{\circ})/n$

Plugging in 10 for yields:

$((10-2)*180^{\circ}/10)=144^{\circ}$

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Example Question #613 : Act Math

Find the total number of degrees inside a hexagon.

Possible Answers:

1080

720

540

900

Correct answer:

720

Explanation:

To solve, simply use the following formula where is the number of sides. Thus,

$\textup{degrees}=(n-2)(180)=(6-2)(180)=4*180=720$

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Example Question #614 : Act Math

Find the total number of degrees in a heptagon.

Possible Answers:

$1080^\circ$

$900^\circ$

$720^\circ$

$540^\circ$

Correct answer:

$900^\circ$

Explanation:

To solve, simply use the formula for finding the degrees in a closed polygon, given n being the number of sides.

In this particular case, a heptagon has seven sides.

Thus,

degrees=(n-2)*180=(7-2)*180=5*180=900

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ACT Math : Other Polygons

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find An Angle In A Polygon

Example Question #2 : How To Find An Angle In A Polygon

Example Question #3 : How To Find An Angle In A Polygon

Example Question #4 : How To Find An Angle In A Polygon

Example Question #5 : How To Find An Angle In A Polygon

Example Question #611 : Act Math

Example Question #612 : Act Math

Example Question #8 : How To Find An Angle In A Polygon

Example Question #613 : Act Math

Example Question #614 : Act Math

All ACT Math Resources

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