A Blank 1 Question 21 with Blank 2 Question 21 sides has a sum of the interior angles of 1980° and each individual angle is
Question
A Blank 1 Question 21 with Blank 2 Question 21 sides has a sum of the interior angles of 1980° and each individual angle is
Solution
The sum of the interior angles of a polygon is given by the formula (n-2) * 180°, where n is the number of sides.
Given that the sum of the interior angles is 1980°, we can set up the equation:
(n-2) * 180° = 1980°
Solving for n gives us:
n - 2 = 1980° / 180° n - 2 = 11 n = 13
So, the polygon (Blank 1) is a 13-gon or tridecagon.
The measure of each individual angle in a regular polygon (where all angles are equal) is given by the formula (n-2) * 180° / n.
Given that the polygon is regular and has 13 sides, we can calculate:
(n-2) * 180° / n = (13-2) * 180° / 13 = 11 * 180° / 13 ≈ 152.31°
So, each individual angle (Blank 2) is approximately 152.31°.
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