Answered

Each exterior angle of a regular decagon has a measure of [tex] (3x + 6)^{\circ} [/tex]. What is the value of [tex] x [/tex]?

A. [tex] x = 8 [/tex]
B. [tex] x = 10 [/tex]
C. [tex] x = 13 [/tex]
D. [tex] x = 18 [/tex]



Answer :

GinnyAnswer
To solve for [tex]\( x \)[/tex] in the given problem, we will follow these steps:

1. Understand the geometry of the problem:
- A regular decagon is a polygon with 10 sides.
- For any regular polygon, the measure of each exterior angle is calculated by dividing 360° by the number of sides.

2. Calculate the measure of each exterior angle of a decagon:
- Since a decagon has 10 sides, each exterior angle of a regular decagon is:
[tex]\[ \frac{360^\circ}{10} = 36^\circ \][/tex]

3. Set up the given equation:
- According to the problem, each exterior angle is given by the expression [tex]\( (3x + 6)^\circ \)[/tex].

4. Equate the two expressions for the exterior angle:
[tex]\[ 3x + 6 = 36 \][/tex]

5. Solve for [tex]\( x \)[/tex]:
- Subtract 6 from both sides of the equation:
[tex]\[ 3x = 36 - 6 \][/tex]
- Simplify the right side:
[tex]\[ 3x = 30 \][/tex]
- Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{30}{3} = 10 \][/tex]

Thus, the value of [tex]\( x \)[/tex] is [tex]\( 10 \)[/tex]. The correct answer is:
[tex]\[ x = 10 \][/tex]

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