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3 years ago

An interior angle of a regular polygon has a measure of 108. What type of polygon is it?

Mathematics

2 answers:

yarga [219]3 years ago

6 0

Answer:

pentagon

Step-by-step explanation:

Recall that for any regular polygon, the number of sides and the interior angles are related through the following formula.

Interior Angle, θ = 180(n-2) / n ; where n is the number of sides

Rearranging :

θ = 180(n-2) / n

nθ = 180 (n-2)

nθ = 180n - 2(180)

nθ = 180n - 360

180n - nθ = 360

n(180 - θ) = 360

n = 360 / (180 - θ) (given that θ = 108°)

n = 360 / (180 - 108)

n = 5

since the polygon has 5 sides, it is a pentagon

sveta [45]3 years ago

4 0

Answer:

pentagon

Step-by-step explanation:

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Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β

Dimas [21]

Answer:

From given relation the value of β is 37.5°

Step-by-step explanation:

Given as :

α and β are two acute angles of right triangle

Acute angle have measure less than 90°

Now given as :

$sin(\frac{x}{2} + 2x)$ = $cos(2x +\frac{3x}{2})$

Or, $cos(90° - (\frac{x}{2}+2x))$ = $cos(2x +\frac{3x}{2})$

SO, $(90° - (\frac{x}{2}+2x))$ = $2x+\frac{3x}{2}$

Or, 90° = $2x+\frac{3x}{2}$ + $\frac{x}{2}+2x$

or, 90° = $\frac{4x}{2}$ + 4x

Or, 90° = $\frac{12x}{2}$

So, x = $\frac{90}{6}$ = 15°

∴ $sin(\frac{x}{2} + 2x)$ = $sin(\frac{15}{2} + 30)$

So, $sin(\frac{x}{2} + 2x)$ = sin $\frac{75}{2}$

∴ The value of Ф_1 = $\frac{75}{2}$ = 37.5°

Similarly $cos(2x +\frac{3x}{2})$ = $cos(30 +\frac{45}{2})$

So ,The value of Ф_2 = $\frac{105}{2}$ = 52.5°

∵ β α

So, As 37.5°52.5°

∴ β = 37.5°

Hence From given relation the value of β is 37.5° Answer

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3 years ago

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jenyasd209 [6]

The expression that represents the number of days until only 10% remains is

T((d) 10%) = 100 • (1/2)^3.322

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3 years ago

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Sveta_85 [38]

: Let y = f(x) = x^1/3
Then dy = 1/3*x^(−2/3) dx
Since f(64) = 4.
We take x = 64 and dx = ∆x = 1
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3 years ago

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Wewaii [24]

3x+4=y+5, then y+5=3x+4
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3 years ago

Jim had some dimes, quarters, and nickels. First, he counted only the dimes and quarters and found that he had 9 coins. Then, he

Olegator [25]

Answer:

$1.90

Step-by-step explanation:

Represent the numbers of nickels, dimes and quarters by n, d and q.

Then: d + q = 9, or q = 9 - d.

Also, n + d = 10

Lastly, n + d + q = 15.

Let's substitute 9 - d for q in the equation immediately above:

n + d + (9 - d) = 15, or n + 9 = 15. Then n must be 6.

In summary, Jim has 6 nickels, (10 - 6) dimes and (9 - 4) quarters, or:

6 nickels, 4 dimes and 5 quarters

Thus, he has 5($0.05) + 4($0.10) + 5($0.25), or

$0.25 + $0.40 + $1.25, or $1.90

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