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tankabanditka [31]
3 years ago
13

A circle has a circumference of 6. It has an arc of length 17/3. What is the central angle of the arc, in degrees?

Mathematics
1 answer:
zepelin [54]3 years ago
7 0

Answer:

340 degrees

Step-by-step explanation:

So the key thing here is to notice that we are given the circumference which will allow us to find a value for the radius of the circle and hence the angle subtended by the arc (the central angle).

So the circumference of a circle = 2pi(r)

This means:

6 = 2pi(r)

Which means that

r = 6/2pi or r = 3/pi

Now we can use this value of r to find our angle in conjunction with the value of the arc length. So:

Arc length is defined by: length = θr

Where θ is our angle value.

So lets plug in:

\frac{17}{3} = (angle)\frac{3}{\pi }

Multiply by pi to get:

\frac{17\pi }{3} = 3(angle)

Divide by 3 to get that:

θ = 17pi/9

So if we convert that from radians to degrees we get 340 degrees.

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What is the measure if each interior angle of a 15-gon
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Answer:

  • The sum of the interior angles of the 15-gon =\:2340^0
  • Each interior angle of the regular polygon =\:156^0

Step-by-step explanation:

As we know that

In any convex polygon, if we may start at one vertex and draw the diagonals to all the other vertices, we would form triangles,

The number of triangles thus formed would always  2  LESS than the number of sides.

As

  • The sum of measure of the angles of any triangle is 180°.

Thus,

The sum of the interior angles of the 15-gon will be:

13\:\times\:180\:=\:2340^0

Also

15-gon is regular, it means this total 2340^0 is shared in equal proportion among the 15 interior angles.

And

Each interior angle of the regular polygon will be:  \frac{2340^{0} }{15}=156^{0}

Therefore, we conclude that:

  • The sum of the interior angles of the 15-gon =\:2340^0
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Keywords: regular polygon, 15-gon, triangle

Learn more about polygon from brainly.com/question/11932357

#learnwithBrainly

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Answer:

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