Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0000 362584 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0775 1213480 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0775 1213480 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1451 4200232 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1463 4227752 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1470 4245464 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1472 4275984 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1481 4298704 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1481 4298704 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1943 4968368 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1978 5160520 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1984 5181448 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.2098 5385384 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.2098 5385640 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

Interior and External Angles of a Regular Polygon In a Given Ratio

Suppose we have an  
\[n\]
  sided regular polygon with the interior and exterior angles in the ratio  
\[11:1\]
.

The interior and exterior angles add up to 180 degrees, so we have to divide 180 in the ratio  
\[11:1\]
.
\[\frac{180}{11+1}=15\]
  degrees.
The interior angle is  
\[11 \times 15 = 165\]
  degrees and the exterior angle is  
\[1 \times 15-15\]
  degrees.
As the perimeter of the polygon is traced out, an angle of 15 degrees is turned through at each vertex.  
\[n\]
  of these turns are made, adding up to a complete turn of 360 degrees. Hence  
\[n=\frac{360}{15}=24\]
.
The polygon has 24 sides.