In 13sided polygon he sum of five angles is 1274 four of the eight angles are equal and the other four is 18° less than each of the equal angles

Question

Find the angles

Answer 1

The sum of the angles of an n-sided polygon is 180(n-2).

For a 13-sided polygon, this means the sum of the angles is 180(13-2) = 180(11) = 1980 degrees

 

We know that

∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 + ∠8 + ∠9 + ∠10 + ∠11 + ∠12 + ∠13 = 1980

 

The sum of 5 angles is 1274.

∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 + ∠8 + ∠9 + ∠10 + ∠11 + ∠12 + ∠13 = 1980

 

[1274] + ∠6 + ∠7 + ∠8 + ∠9 + ∠10 + ∠11 + ∠12 + ∠13 = 1980

 

∠6 + ∠7 + ∠8 + ∠9 + ∠10 + ∠11 + ∠12 + ∠13 = 706

 

Four of the eight remaining angles are equal - let them be x

The other four are 18 degrees less than the equal angles - so they will be x - 18

 

x + x + x + x + x - 18 + x - 18 + x - 18 + x - 18 = 706

8x - 72 = 706

8x = 778

x = 97.25.

 

To summarize, you have 4 angles that measure 97.25 degrees.  

There are four other angles that measure 97.25 - 18 which is 79.25 degrees.

 

The other five angles you cannot know for certain, but their sum is 1274.

 

Hope this helps.  :)