PSAT Math help » Geometry » aircraft Geometry » circles » Sectors » exactly how to find the edge of a sector

A pie has actually a diameter that 12\". A item is reduced out, having a surface ar area the 4.5π. What is the angle of the cut?


Explanation:

This is simply a issue of percentages. We an initial have to number out what portion of the surface ar area is represented by 4.5π. To do that, we must calculate the full surface area. If the diameter is 12, the radius is 6. Don\"t be tricked by this!

A = π * 6 * 6 = 36π

Now, 4.5π is 4.5π/36π percent or 0.125 (= 12.5%)

To number out the angle, we need to take that portion of 360°:

0.125 * 360 = 45°


Eric is riding a Ferris wheel. The Ferris wheel has actually 18 compartments, numbered in stimulate clockwise. If compartment 1 is in ~ 0 degrees and Eric beginning compartment 13, what angle is the at?


 

 

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In the figure over that contains Circle O, the measure up of angle BAC is equal to 35 degrees, the measure of edge FBD is equal to 40 degrees, and the measure up of arc advertisement is twice the measure up of arc AB. I beg your pardon of the complying with is the measure up of edge CEF? The figure is not necessarily drawn to scale, and the red numbers are used to note the angles, not stand for angle measures.

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Explanation:

The measure of edge CEF is going to be equal to half of the difference between the procedures two arcs the it intercepts, specific arcs advertisement and CD.

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Thus, we need to uncover the measure of arcs ad and CD. Let\"s look in ~ the info given and also determine just how it can help us figure out the measures of arcs ad and CD. 

Angle BAC is an enrolled angle, which way that the meausre is one-half the the measure of the arc the it incercepts, i m sorry is arc BC.

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Thus, since angle BAC is 35 degrees, the measure up of arc BC should be 70 degrees.

We have the right to use a similar strategy to discover the measure of arc CD, which is the arc intercepted by the inscribed edge FBD.

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Because edge FBD has a measure up of 40 degrees, the measure of arc CD should be 80 degrees.

We have actually the measures of arcs BC and CD. But we still require the measure of arc AD. We can use the last piece of information given, along with our knowledge around the amount of the arcs the a circle, to determine the measure of arc AD.

We space told the the measure of arc ad is double the measure up of arc AB. We likewise know the the sum of the steps of arcs AD, AB, CD, and also BC must be 360 degrees, since there space 360 degrees in a complete circle. 

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Because ad = 2AB, we deserve to substitute 2AB because that AD.

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This means the measure of arc ab is 70 degrees, and also the measure of arc advertisement is 2(70) = 140 degrees.

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Now, we have all the information we require to uncover the measure of angle CEF, i m sorry is equal to half the difference in between the measure up of arcs advertisement and CD.