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°
The second survey is more believable because there is randomness in the second rather than the first survey. Since the second company surveyed in all interest levels while the first company only surveyed their best customers. Random sampling like what the second company did helps produce representative samples by removing voluntary response bias and undercover age bias.
