in a 13-sided polygon the sum of 5 angles is 1274 degree four of the eight angles remaining are equal and the other 4 are 18 degree less than each of the equal angles find the angles

Answer 1

The sum of the interior angles of a 13-sided polygon is given by:

Sum = (13-2) x 180 = 1980 degrees

Let x be the measure of the equal angles. Then, we have:

5x + 4y + 4(z-18) = 1274 (where y is the measure of the four equal angles, and z is the measure of the other four angles that are 18 degrees less than each of the equal angles)

x + y + z = 1980/13

We have two equations with two variables, so we can solve for x and y.

First, we can simplify the first equation by combining like terms:

5x + 4y + 4z - 72 = 1274

5x + 4y + 4z = 1346

Next, we can use the second equation to solve for z in terms of x and y:

z = 1980/13 - x - y

Substituting this into the first equation, we have:

5x + 4y + 4(1980/13 - x - y) = 1346

Simplifying and solving for y, we get:

y = (1980/13 - x - 169)/2

Now we can substitute this expression for y back into the equation for z:

z = 1980/13 - x - (1980/13 - x - 169)/2

Simplifying, we get:

z = 845/13 - x + 169/2

Now we can substitute our expressions for y and z back into the equation for the sum of the angles:

5x + 4[(1980/13 - x - 169)/2] + 4[845/13 - x + 169/2 - 18] = 1274

Simplifying and solving for x, we get:

x = 155

Substituting this value back into our expressions for y and z, we get:

y = 67

z = 100

Therefore, the angles of the 13-sided polygon are:

155, 67, 100, 100, 100, 100, 152, 152, 152, 152, 133, 133, 133

Answer 2

Totally disagree.

The sum of all 13 angles is indeed 1980
5 of them add up to 1274
4 of them are equal, call each one x
4 of the are each 18 less than x, so x-18

4x + 4(x-18) + 1274 = 1980
4x + 4x - 72 + 1274= 1980
8x = 778
x = 97.25

So we have 4 angles of 97.25° each, 4 angles of 79.25° and 5 other
angles whose sum is 1274°

check:
4(97.25) + 1(79.25) + 1274 = 1980

the bot has 4 angles of 100°, 4 angles of 152°, and then 5 others.
That sum is 1562° , not the 1980° we need
btw, there is no way that we know anything about the first 5 angles other
than they add up to 1274

Answer 3

I apologize for the error in the previous response. You are correct that the sum of the 13 angles must add up to 1980 degrees, and we cannot determine the values of the first 5 angles. Your solution is the correct one. Thank you for pointing out the mistake.