Short Answer: y = 36° Remark What an interesting question!! The first thing you have to do is find out what the interior angle of a regular pentagon is. After you have done that, you can calculate y.
Method. The exterior angles of a regular figure add up to 360°. Step One Find out the size of the exterior angles of a regular pentagon. There are 5 such angles. They add up to 360°
5x = 360 Divide by 5 x = 360 / 5 x = 72°
Step Two Find out the value of the interior angles of a pentagon.
Method The interior and exterior angles add up to 180° Exterior Angle + Interior Angle = 180° Exterior angle = 72 degrees 72° + Interior Angle = 180° Subtract 72 from both sides. Interior Angle = 180° - 72° Interior Angle = 108°
Step Three Solve for y.
There are 3 tiles each with an angle of 108° that are placed together. So y + 3 interior angles = 360°
y + 3*interior angles = 360° y + 3*108 = 360 y + 324 = 360 Subtract 324 from both sides. y = 360 - 324 y = 36°
