a.
Tocalculate:The sum ofmeasure of
a.
Answer to Problem 26CR
Thesum of measure of polygons angles is
Explanation of Solution
Given information:
A polygons with angles A, B, C, D, and E.
Formula used:
The below theorem is used:
The exterior angle theorem states that the measure of an exterior angle of a
Calculation:
By exterior angle theorem, we get
Sum of angles in a triangle is
Adding Equation 1, Equation 2 and Equation 3, we get
b.
To find: The sum of angles measured depends on equilateral or equiangular polygons.
b.
Answer to Problem 26CR
No,sum of angles measured does not depends on equilateral or equiangular polygons.
Explanation of Solution
Given information:
A polygons with angles A, B, C, D, and E.
Formula used:
The below theorem is used:
The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Calculation:
By exterior angle theorem, we get
Sum of angles in a triangle is
Adding Equation 1, Equation 2 and Equation 3, we get
Equilateral polygons are those whose all sides are equal.
Equiangular polygons are those whose all angles are equal.
We use exterior angle theorem to find the sum of angles.
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