At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine the value of [tex]\( x \)[/tex] for the given problem, we need to follow a systematic approach.
1. Understand Exterior Angles of a Regular Polygon:
The sum of the exterior angles of any polygon is always [tex]\( 360^\circ \)[/tex]. For a regular polygon (a polygon with all sides and angles equal), each exterior angle can be calculated by dividing [tex]\( 360^\circ \)[/tex] by the number of sides [tex]\( n \)[/tex].
2. Calculate the Exterior Angle for a Regular Decagon:
A regular decagon has 10 sides. Thus, each exterior angle of a regular decagon can be calculated as:
[tex]\[ \text{Exterior angle} = \frac{360^\circ}{10} = 36^\circ \][/tex]
3. Set Up the Equation:
We are given that each exterior angle is [tex]\((3x + 6)^\circ\)[/tex]. Therefore, we can set up the equation:
[tex]\[ 3x + 6 = 36 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we need to solve the equation [tex]\( 3x + 6 = 36 \)[/tex]:
[tex]\[ 3x + 6 = 36 \][/tex]
Subtract 6 from both sides:
[tex]\[ 3x = 30 \][/tex]
Divide both sides by 3:
[tex]\[ x = 10 \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 10 \)[/tex].
Thus, the correct answer is:
[tex]\[ x = 10 \][/tex]
which matches the solution provided.
1. Understand Exterior Angles of a Regular Polygon:
The sum of the exterior angles of any polygon is always [tex]\( 360^\circ \)[/tex]. For a regular polygon (a polygon with all sides and angles equal), each exterior angle can be calculated by dividing [tex]\( 360^\circ \)[/tex] by the number of sides [tex]\( n \)[/tex].
2. Calculate the Exterior Angle for a Regular Decagon:
A regular decagon has 10 sides. Thus, each exterior angle of a regular decagon can be calculated as:
[tex]\[ \text{Exterior angle} = \frac{360^\circ}{10} = 36^\circ \][/tex]
3. Set Up the Equation:
We are given that each exterior angle is [tex]\((3x + 6)^\circ\)[/tex]. Therefore, we can set up the equation:
[tex]\[ 3x + 6 = 36 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we need to solve the equation [tex]\( 3x + 6 = 36 \)[/tex]:
[tex]\[ 3x + 6 = 36 \][/tex]
Subtract 6 from both sides:
[tex]\[ 3x = 30 \][/tex]
Divide both sides by 3:
[tex]\[ x = 10 \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 10 \)[/tex].
Thus, the correct answer is:
[tex]\[ x = 10 \][/tex]
which matches the solution provided.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.