What is the sum of the measures of the angles of a regular decagon? What is the measure of each angle in the decagon?
1,620°; 162°
2,880°; 288°
1,440°; 144°
none of these
it is free
the sum of the EXTERIOR angles of a polygon is 360º
decagon has 10 sides (and angles)
each exterior angle is ... 360º /10
each interior angle is ... 180º - (360º /10)
For a polygon of n sides, the sum of the interior angles is
180(n-2)
To find the sum of the measures of the angles of a regular decagon, you can use the formula:
Sum of angles = (n - 2) * 180°
where "n" represents the number of sides in the polygon. For a regular decagon with 10 sides, the formula becomes:
Sum of angles = (10 - 2) * 180°
Sum of angles = 8 * 180°
Sum of angles = 1,440°
Therefore, the sum of the measures of the angles of a regular decagon is 1,440°.
To find the measure of each angle in the decagon, divide the sum of the angles by the number of sides:
Measure of each angle = Sum of angles / Number of sides
Measure of each angle = 1,440° / 10
Measure of each angle = 144°
So, the measure of each angle in a regular decagon is 144°.
Therefore, the correct answer is "1,440°; 144°".