This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey, good to see you again. Step 1: Calculate the interior angle of a regular pentagon. A regular pentagon has n=5 sides. The formula for the interior angle of a regular n-sided polygon is ((n-2) × 180^)/(n). EAB = ((5-2) × 180^)/(5) = (3 × 180^)/(5) = (540^)/(5) = 108^ a) 108^ Step 2: Calculate ABN. In a regular pentagon, all sides are equal in length. Therefore, EA = AB. This means EAB is an isosceles triangle. The base angles of an isosceles triangle are equal. So, ABE = AEB. The sum of angles in a triangle is 180^. EAB + ABE + AEB = 180^ 108^ + 2 × ABE = 180^ 2 × ABE = 180^ - 108^ 2 × ABE = 72^ ABE = (72^)/(2) = 36^ Since N lies on EB, ABN = ABE. b)