Use this diagram of a regular pentagon to explain how to determine the formula for finding the vertex angle in a regular polygon.


Divide the pentagon into three triangles.The sum of the degree measures
of the three triangles is the same as the sum of the degree measures of the
vertex angles of the regular pentagon. Since each vertex angle in the regular.

pentagon is the same, 5v = 180° X 3; V = 180° X 3 / 5. Since 3 = n - 2 for n =5; in general you can see that for a regular n-gon, the measure of the vertex angle is v = 180° x (n-2)/n.

Mathematics

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Evaluate the integral.

A. cos-1  + C
B. -sin-1  + C
C. sin-1  + C
D.  + C

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Find the unknown length in the right triangle. If necessary, round to the nearest tenth.

A. 4.4 cm B. 7.7 cm C. 13.8 cm D. 191.1 cm

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Solve.How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 8 members?

A. 24 B. 1680 C. 70 D. 32

Mathematics

Find the slope-intercept equation for the tangent line to the graph of f at the given point.f(x) =  at (25, 5)

A. y = x + 
B. y = x - 
C. y = x + 4
D. y = - x + 

Mathematics