Answer :
To find the measure of each interior angle of a regular polygon when the sum of the interior angles is given, we can use the formula: Sum of Interior Angles=(n−2)×180 Where: - n is the number of sides of the polygon - The sum of interior angles of a polygon with n sides is (n−2)×180 degrees Given that the sum of the interior angles of the regular polygon is 5040, we can set up the equation:
(n−2)×180=5040 Solving for n: n−2=1805040n−2=28n=30 Therefore, the regular polygon has 30 sides.
To find the measure of each interior angle of the regular polygon, we use the formula for the measure of each interior angle of a regular polygon: Measure of Each Interior Angle=nSum of Interior Angles Substitute the values: Measure of Each Interior Angle=305040=168 degrees
Therefore, each interior angle of the regular polygon measures 168 degrees.
