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3 years ago

the measure of an interior angel of a regular polygon is 150. find the number of sides in the polygon.

Mathematics

1 answer:

adoni [48]3 years ago

5 0

Answer:

The polygon has $12$ sides.

Step-by-step explanation:

Recall that the expression for finding the measure of one interior angle of a regular polygon is $\frac{180(n-2)}{n}$ , where $n$ is the number of sides the polygon has (and $n\neq 0$ ), which is what we want to find.

Because the measure of one interior angle of the given polygon is $150\textdegree$ , we can write the following equation to solve for $n$ :

$\frac{180(n-2)}{n}=150$

Solving for $n$ , we get:

$\frac{180(n-2)}{n}=150$

$\frac{180n-360}{n}=150$ (Distribute the $180$ in the numerator)

$180n-360=150n$ (Multiply both sides of the equation by $n$ to eliminate the denominator and simplify)

$30n-360=0$ (Subtract $150n$ from both sides of the equation and simplify)

$30n=360$ (Add $360$ to both sides of the equation to isolate $n$ and simplify)

$\bf n=12$ (Divide both sides of the equation by $30$ to get rid of $n$ 's coefficient and simplify)

Therefore, the polygon has $\bf 12$ sides. Hope this helps!

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<h3>How to calculate temperature?</h3>

The quantity or amount of radiation contained in material or item, as measured by a temperature or sensed by touch and stated on a numerical scale.

The temperature T of a ball bearing is inverse to the length first from the origin, which we consider to be the center of the ball. The temperature at the exact location

(x, y, z) is a point on the sphere, the temperature at this point is given by

$T(x,y,z)= \dfrac{k}{(x^2 +y^2+z^2)^{1/2}}$

Where k is constant, then we have

T(1, 2, 2) = k/3 = 170

k = 510

$T(x,y,z)= \dfrac{510}{(x^2 +y^2+z^2)^{1/2}}$

Then we have

$\rm \triangledown T = \left ( -\dfrac{510x}{(x^2 +y^2+z^2)^{1/2}}, -\dfrac{510y}{(x^2 +y^2+z^2)^{1/2}}, \dfrac{510z}{(x^2 +y^2+z^2)^{1/2}} \right )\\\\\\\triangledown T (1, 2, 2) = -\dfrac{510}{27} (1, 2, 2) =-\dfrac{170}{9} (1, 2, 2)$

Then the direction will be from (1, 2, 2) to (4, 3, 5) will be (3, 1, 3)

So u = (3/√19, 1/√19, 3/√19)

Then we get

$\rm \triangledown T \cdot u = \dfrac{-170}{9}(1, 2, 2) \cdot \left (\dfrac{3}{\sqrt{19}}, \dfrac{1}{\sqrt{19}}, \dfrac{3}{\sqrt{19}} \right )\\\\\\\triangledown T \cdot u = - \dfrac{170}{9\sqrt{19}} (3 + 2 + 6)\\\\\\\triangledown T \cdot u = -\dfrac{1870}{9\sqrt{19}}$

The direction of the greatest inverse in the temperature is given by any vector parallel to and having the same direction $\triangledown$ T. (-x, -y, -z) the vector form (x, y, z) to the origin, in the direction of the greatest increase.