In a 13-sided polygon, the sum of five angles is 1274degrees .four of the eight angles remaining are equal and the other four are 18degree less than each of the equal angles .find the angles

Answer 1

Let x be the measure of the equal angles.

Then the four angles that are 18 degrees less than the equal angles are x - 18.

The sum of all the angles in a 13-sided polygon is (13-2) * 180 = 1980 degrees.

Given that the sum of five angles is 1274 degrees, we can set up the following equation:

5x + 4(x - 18) + 4(x) = 1274
5x + 4x - 72 + 4x = 1274
13x - 72 = 1274
13x = 1346
x = 103.54

So, the equal angles are approximately 103.54 degrees.

The four angles that are 18 degrees less than the equal angles are x - 18, which is approximately 85.54 degrees.

Therefore, the angles in the 13-sided polygon are:
5 angles = 5 * 103.54 = 517.7 degrees
4 equal angles = 4 * 103.54 = 414.2 degrees
4 angles that are 18 degrees less = 4 * 85.54 = 342.2 degrees