Question 1161248
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If you want to find an "angel", either at the center of a sector or anywhere else, I suggest you consult your local priest, pastor, holy man, tribal shaman, or whatever floats your particular boat.


If you want the central <b>angle</b> of a sector of a circle with radius 21 cm where the perimeter of the sector, i.e. 2 times the circle radius plus the measure of the subtended arc is 53 cm, then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2r\ +\ arc\ =\ 53]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ arc\ =\ 53\ -\ 42\ =\ 11]


So the arc length is 11 cm.


The circumference of the entire circle is *[tex \Large 2\pi{r}] and the radian measure of the entire circle is *[tex \Large 2\pi].  The angle measure of the central angle of the sector ("CA") is in proportion to the radian measure of the entire circle as the arc length is to the circumference:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{CA}{2\pi}\ =\ \frac{11}{42\pi}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ CA\ =\ \frac{11}{21}\ ] radians.


for an approximate value in degrees multiply by 180 and divide by a convenient approximation of *[tex \Large \pi]
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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