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VARVARA [1.3K]
3 years ago
8

How to find the measure of an interior angle of an irregular polygon?

Mathematics
1 answer:
adelina 88 [10]3 years ago
7 0
<span><span>


</span> <span> Exterior Angles of a Polygon Definition: the angle formed by any side of a polygon and the extension of its adjacent side Try this Adjust the polygon below by dragging any orange dot. Click on "make regular" and repeat. Note the behavior of the exterior angles and their sum. <span> </span> Regular polygons In the figure above check "regular". As you can see, for regular polygons all the exterior angles are the same, and like all polygons they add to 360° (see note below). So each exterior angle is 360 divided by the n, the number of sides. As a demonstration of this, drag any vertex towards the center of the polygon. You will see that the angles combine to a full 360° circle. Convex case In the case of convex polygons, where all the vertices point "outwards" away form the interior, the exterior angles are always on the outside of the polygon. In the figure above, check "regular" and notice that this is the case. Although there are two possible exterior angles at each vertex (see note below) we usually only consider one per vertex, selecting the ones that all go around in the same direction, clockwise in the figure above. Taken one per vertex in this manner, the exterior angles always add to 360° This is true no matter how many sides the polygon has, and regardless of whether it is regular or irregular, convex or concave. In the figure above, adjust the number of sides, switch to irregular and drag a vertex to see that this is true. In the figure above click on 'reset' and check "both". You will see that both angles at each vertex are always congruent (same measure). This is because they form a pair of vertical angles, which are always congruent. Drag the vertices around and convince yourself this is true. Concave case If the polygon is concave, things are a little trickier. A concave polygon has one or more vertices "pushed in" so they point towards the interior. In the figure above, uncheck "regular" and drag a vertex in towards the interior of the polygon. Notice that the exterior angle flips over into the inside of the polygon and becomes negative. If you add the exterior angles like before, they still add to 360°, you just have to remember to add the negative angles correctly. Exterior and Interior angles are supplementary At any given vertex, the interior angle is supplementary to an exterior angle. See Interior/Exterior angle relationship in a polygon. Walking the polygon In the figure above, imagine the polygon drawn on the ground. Stand on one of the sides and face along the line. Now if you walk around the polygon along each line in turn, you will eventually wind up back where you started, facing the same way. So you must have turned through a total of 360°, a full circle. This confirms that the exterior angles, taken one per vertex, add to 360° The sum of exterior angles - watch out! In most geometry textbooks they say flatly that the exterior angles of a polygon add to 360° This is only true if: <span> You take only one per vertex, and Take all the angles that point in the same direction around the polygon. </span> But in many cases they fail to state these conditions. In the figure at the top of the page, check the "Both" checkbox. You will see there are two per vertex and they actually add to 720° (360 times 2) So if you are asked "What is the sum of the exterior angles of a polygon?" without any conditions, you will have to guess which one they mean. Usually they mean taking one per vertex, and the answer is 360°, although strictly speaking this is wrong. </span></span>
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Solve for the indicated variable. Include all of your work in your answer. Submit your solution. P = 3r + 2s; for s.
madam [21]
<h3>Given</h3>

P = 3r + 2s

<h3>Find</h3>

the corresponding equation for s

<h3>Solution</h3>

First of all, look at how this is evaluated in terms of what happens to a value for s.

  1. s is multiplied by 2
  2. 3r is added to that product

To solve for s, you undo these operations in reverse order. The "undo" for addition is adding the opposite. The "undo" for multiplication is division (or multiplication by the reciprocal).

... P = 3r + 2s . . . . . . starting equation

... P - 3r = 2s . . . . . . -3r is added to both sides to undo addition of 3r

... (P -3r)/2 = s . . . . . both sides are divided by 2 to undo the multiplication

Note that the division is of everything on both sides of the equation. That is why we need to add parentheses around the expression that was on the left—so the whole thing gets divided by 2.

Your solution is ...

... s = (P - 3r)/2

3 0
3 years ago
Given the functions f(x) = 7x + 13 and g(x) = x + 2, which of the following functions represents f[g(x)] correctly? (2 points)
Svetach [21]

Answer:

The value of f[ g(x) ] = 7x + 27

Step-by-step explanation:

It is given that, f( x ) = 7x + 13 and g( x ) = x + 2

<u>To find the value of f(g(x))</u>

g(x) = x + 2 and 7x + 13   (given)

Let g(x) = x + 2

f [ g(x) ] = 7(x + 2) + 13  [ substitute the value of g(x) in f(x) ]

 = 7x + 14 + 13

 = 7x + 27

Therefore the value of f[ g(x) ] = 7x + 27

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According to the CDC, the rate of Cesarean births in the United States in 2013 was about 33%. Suppose a random sample of 200 bir
sergij07 [2.7K]

Answer:

n = 200

p = 0.33.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

33% of the births are Cesarean, so p = 0.33

Sample of 200 births, which eans that, n = 200

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