Suppose the interior angles of a convex pentagon are five consecutive numbers, find....?

Question

the measure of the largest angle

Answer 1

The equation:

(x - 4) + (x - 3) + (x - 2) + (x - 1) + x = 180 .(5 - 2)

5x - 10 = 540

5x = 550

x = 110

You're welcome.

Answer 2

A convex pentagon has an indoors attitude sum equivalent to (n-2)*one hundred eighty the place n = form of facets (5-2)*one hundred eighty = 540 as a results of fact that they are consecutive numbers enable the angles be x x+a million x+2 x+3 x+4 upload the angles and set it equivalent to 540 x + (x +a million) + (x +2) + (x +3) + (x+4) = 540 5x + 10 = 540 5x = 530 x = 106 So the degree of the biggest is x + 4 106 + 4 a hundred and ten tiers

Answer 3

Assuming you meant degrees and not radians :-) the sum of the n interior angles of a convex n-gon would be 180 (n - 2) degrees so if the five consecutive degree measures were x -2 through x + 2 then 5x = 180 * 3 degrees or x = 108 degrees is the middle angle.

So the largest interior angle is 110 degrees.

Answer 4

Let the measure of the angles of a 5-sided polygon from smallest to largest be a, b, c, d, e and let them be consecutive, what are the angles?

This is 5 equations and 5 unknowns:
a+b+c+d+e=180
b=a+1
c=b+1
d=c+1
e=d+1

You could solve these equations if you wanted to, but its some work.

if you think about it.. the average of a through e is going to be the same as an interior angle in a regular pentagon... 36 degrees.
so you can know that c is 36, d is 37 and e is ... 38

Answer 5

x +x+1 +x+2 +x+3 +x+4 = 180 (5-2)

5x +10 = 540
5x = 530
x= 106 degrees

the largest is x+4 = 106+4 = 110

Answer 6

110°
rotflol