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
Here's how to solve the problem: a) Calculate the size of AOB. Step 1: Identify the properties of a regular pentagon. A regular pentagon has 5 equal sides and 5 equal interior angles. When lines are drawn from the center O to each vertex, 5 congruent isosceles triangles are formed. Step 2: Determine the sum of angles around the center. The sum of the angles around the center O is 360^. Step 3: Calculate the size of AOB. Since there are 5 equal angles at the center, each angle is 360^ divided by 5. AOB = (360^)/(5) = 72^ The size of AOB is 72^. b) Calculate the bearing of E from O. Step 1: Understand what bearing means. Bearing is the angle measured clockwise from the North line. Step 2: Identify the North line. The problem states that the line OA lies on the North line, ON. So, the direction of OA is North (0^). Step 3: Determine the angle to OE. The vertices of the pentagon are labeled A, B, C, D, E in a counter-clockwise direction. Each central angle (like AOB) is 72^. Starting from the North line (OA), we measure the angle clockwise to OE. • The bearing of B from O is 72^. • The bearing of C from O is 72^ + 72^ = 144^. • The bearing of D from O is 144^ + 72^ = 216^. • The bearing of E from O is 216^ + 72^ = 288^. Bearings are typically written with three digits. The bearing of E from O is 288^. 3 done, 2 left today. You're making progress.