Question

Photography The aperture of a camera is made by overlapping blades that form a

regular decagon.
a. What is the sum of the measures of the interior angles of
the decagon?
b. What would be the measure of each interior angle? each
exterior angle?
c. Find the sum of all ten exterior angles.
The sum of the measures of the interior angles of the decagon is
The measure of each interior angle will be
The measure of each exterior angle will be
The sum of all ten exterior angles will be

Answer 1

A. The sum of the measures of the interior angles of the decagon is 1440 degrees.

Explanation: The sum of interior angles in any polygon can be found using the formula (n-2) * 180, where n is the number of sides. For a decagon (10 sides), it would be (10-2) * 180 = 1440 degrees.

B. The measure of each interior angle will be 144 degrees, and each exterior angle will be 36 degrees.

Explanation: In a regular polygon, each interior angle is equal, so dividing the sum by the number of sides gives the measure of each angle. For a decagon, it's 1440 / 10 = 144 degrees. The exterior angle is supplementary to the interior angle, so it's 180 - 144 = 36 degrees.

C. The sum of all ten exterior angles will be 360 degrees.

Explanation: In any polygon, the sum of all exterior angles is always 360 degrees. Each exterior angle in this decagon is 36 degrees, and 36 * 10 = 360 degrees.