How is polygon described?

What is the angle of each interior angle in a polygon with 19 sides?

• This is the question A regular polygon has 19 sides. Find the size of each interior angle. Could you answer any of these either? Each exterior angle of a regular polygon is 15 degrees. How many sides does the polygon have? The sum of the interior angles of a polygon is 1800 degrees. How many sides does the polygon have?

• Answer:

  The sum of all angles in a polygon is given by the formula sum of angles = ( n - 2 ) x 180 .......(n is the number of sides) {REMEMBER THIS} so in your case: sum of angles = ( 19 - 2 ) x 180 = 17 x 180 = 3060 degrees now the concerned polygon has 19 angles, so the measure of each angle will be: 3060 / 19 = 161.05 (approx). Second problem: how on earth can an exterior angle be 15 degrees? It might be 180-15 = 165 degrees Therefore the problem can be solved by this equation: sum of angles = ( n - 2 ) x 180 so 165 x n = ( n -2 ) x 180 ....................... (solve this equation) therefore n=24 so the polygon has 24 sides. Third Problem: sum of angles = ( n - 2 ) x 180 1800 = (n - 2) x 180 ..... solve this equation n = 12 the polygon has 12 sides.