The sum of the measures of the interior angles of a decagon (10 sided polygon) is 1,440. We found this by using the formula (n-2)(180). Thus, to find the measure of each interior angle we simply divide the sum by the number of total sides in the polygon. 1,440/10 = 144.
What is one exterior angle of a decagon?
Since each exterior angle and interior angle form a linear pair, one exterior angle of a decagon = 180 – 144 = 36°.
What angle do you cut for a decagon?
Decagon Definitions
A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144° and they all add up to 1,440° .
What is the sum of angle of a convex polygon with 10 sides?
Answer: The sum of angles in a convex 10-sided polygon is equal to 1440°. We will use the shape of the decagon to find the sum of angles.
What is the value of one interior angle of a regular decagon?
The sides and angles are congruent in a regular decagon. The characteristics of a regular decagon are: All sides are equal in length and all the angles are equal in the measure in a regular decagon. Each interior angle in regular decagon measures 144º, while each exterior angle measures 36º.
What is the size of one interior angle of a dodecagon?
Each interior angle of a regular dodecagon is equal to 150°. Each exterior angle of a regular dodecagon is equal to 30°.
How do you find the radius of a decagon?
r = s/2sin(180/n) where r is the radius, s is the length of any side, n is the number of sides and the angle measure is in degrees.
What is the sum of the interior angles of a convex polygon of 12 sides?
Dodecagon is a 12-sided polygon with 12 angles and 12 vertices. The sum of the interior angles of a dodecagon is 1800°.
What is the angle sum of convex polygon with number of 12 sides?
Correct answer:
Explanation: The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.
How do you find the sum of the interior angles of a convex polygon?
Theorem 39: If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = ( n −2) × 180°.
