SOLUTION: For each of the convex polygons of n sides, find the measure of the largest interior angle. a. n=10, the smallest interior angle measures 100 degrees and the angles increase i

Algebra ->  Length-and-distance -> SOLUTION: For each of the convex polygons of n sides, find the measure of the largest interior angle. a. n=10, the smallest interior angle measures 100 degrees and the angles increase i      Log On


   

Question 364488: For each of the convex polygons of n sides, find the
measure of the largest interior angle.
a. n=10, the smallest interior angle measures 100 degrees
and the angles increase in an arithmetic
sequence.
b. n=5, the measures of the angles are labeled x,
y, z, u, v, where is of y = 2x , z is 3/5 of y, u is 4/5 of z , and v = z.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

Sum of the angles in a convex polygons of n sides is 180(n-2) degrees

n = 10

180° * 8 = 1440°

smallest is 100° & angles increase in an arithmetic sequence.

S = (n/2)(2a + (n-1)d)

1440 = 5 (200 + 9d)

288 = 200 + 9d

88 = 9d

a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d

a%5B10%5D+=+100+%2B+88  

a%5B10%5D+=+188



n= 5

180° * 3 = 540°

540° = x +  y +   z     +     u         +   v

540° = x + 2x + (3/5)2x + (4/5)(3/5)2x  + (3/5)2x

simplify and solve for x

25* 540° = x + 2x + + (6/5)x + (24/25)x + (6/5)x 

25* 540° = 25x + 50x + + 30x +  24x + 30x 

25*540 = 159x

84.9 = x

largest is 2x = 169.8 degrees