Each Exterior Angle Of A Regular Decagon Has A Measure Of $(3x+6)^{\circ}$. What Is The Value Of $x$?A. $x = 8$ B. $x = 10$ C. $x = 13$ D. $x = 18$
Introduction
A regular decagon is a polygon with 10 equal sides and 10 equal angles. Each exterior angle of a regular decagon has a measure of $(3x+6)^{\circ}$. In this article, we will solve for the value of $x$ using the properties of regular polygons.
Properties of Regular Polygons
A regular polygon is a polygon that has equal sides and equal angles. The sum of the exterior angles of any polygon is always 360 degrees. Since a regular decagon has 10 equal exterior angles, each exterior angle measures $(360/10)^{\circ} = 36^{\circ}$.
Equating the Exterior Angle Measures
Since each exterior angle of a regular decagon has a measure of $(3x+6)^{\circ}$, we can set up an equation to equate this measure to the known measure of 36 degrees:
Solving for x
To solve for $x$, we need to isolate $x$ on one side of the equation. We can start by subtracting 6 from both sides of the equation:
Next, we can divide both sides of the equation by 3:
Conclusion
In this article, we solved for the value of $x$ in a regular decagon using the properties of regular polygons. We equated the exterior angle measures and solved for $x$ to find that $x = 10^{\circ}$.
Answer
The value of $x$ is $10^{\circ}$.
Comparison with Answer Choices
Introduction
In our previous article, we solved for the value of $x$ in a regular decagon using the properties of regular polygons. In this article, we will answer some frequently asked questions related to the problem.
Q: What is a regular decagon?
A regular decagon is a polygon with 10 equal sides and 10 equal angles.
Q: What is the sum of the exterior angles of any polygon?
The sum of the exterior angles of any polygon is always 360 degrees.
Q: Why is each exterior angle of a regular decagon equal to 36 degrees?
Since a regular decagon has 10 equal exterior angles, each exterior angle measures $(360/10)^{\circ} = 36^{\circ}$.
Q: How do we equate the exterior angle measures in the problem?
We equate the exterior angle measures by setting up an equation: $(3x+6)^{\circ} = 36^{\circ}$.
Q: How do we solve for x in the equation?
To solve for $x$, we need to isolate $x$ on one side of the equation. We can start by subtracting 6 from both sides of the equation, then dividing both sides by 3.
Q: What is the value of x in the problem?
The value of $x$ is $10^{\circ}$.
Q: Why is the value of x equal to 10 degrees?
The value of $x$ is equal to 10 degrees because we solved for $x$ by equating the exterior angle measures and isolating $x$ on one side of the equation.
Q: What is the relationship between the exterior angle measures and the number of sides of a polygon?
The exterior angle measures of a polygon are related to the number of sides of the polygon. In a regular polygon, each exterior angle measures $(360/n)^{\circ}$, where $n$ is the number of sides.
Q: Can we use the same method to solve for x in other regular polygons?
Yes, we can use the same method to solve for $x$ in other regular polygons by equating the exterior angle measures and solving for $x$.
Conclusion
In this article, we answered some frequently asked questions related to the problem of solving for the value of $x$ in a regular decagon. We hope that this article has provided a better understanding of the problem and its solution.
Frequently Asked Questions
- What is a regular decagon?
- What is the sum of the exterior angles of any polygon?
- Why is each exterior angle of a regular decagon equal to 36 degrees?
- How do we equate the exterior angle measures in the problem?
- How do we solve for x in the equation?
- What is the value of x in the problem?
- Why is the value of x equal to 10 degrees?
- What is the relationship between the exterior angle measures and the number of sides of a polygon?
- Can we use the same method to solve for x in other regular polygons?