1. The measure of angles of a pentagon is represented by x, 2x, 2x+20, 3x-5, and 2x+15. what is the value of x?
2. Given the figure below, what is the value of x?
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1. The measure of angles of a pentagon is represented by x, 2x, 2x+20, 3x-5, and 2x+15. what is the value of x?
2. Given the figure below, what is the value of x?
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1. The measure of angles of a pentagon is represented by x, 2x, 2x+20, 3x-5, and 2x+15. What is the value of x?
The sum of the interior angles of a polygon is defined as:
∑ = (n - 2)180°
In this case, the polygon is a pentagon, hence set n = 5, so
∑ = (5 - 2)180°
= (3)180°
= 540°
Hence, the interior angles of a pentagon have a sum of 540°.
The measure of the angles is represented by x, 2x, 2x + 20, 3x - 5, and 2x + 15, so we'll equate the sum of it to 540.
x + (2x) + (2x + 20) + (3x - 5) + (2x + 15) = 540
--> 10x + 30 = 540
--> 10x = 510
--> x = 51
Therefore, the value of x is 51.
2. Given the figure below, what is the value of x?
Notice that the sides of the angles (x + 17) and (2x - 15) form a capital N.
By definition, the sides of alternate interior angles form a capital N or Z in varying positions, and these angles are congruent.
This implies that (x + 17) and (2x - 15) are alternate interior angles, so that
x + 17 = 2x - 15
--> 2x - x = 17 + 15
--> x = 32
Therefore, the value of x is 32.
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