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
B. 160^ Step 1: Find the measure of angle BAC. The sum of angles in a triangle is 180^. In ABC: m( BAC) + m( ABC) + m( ACB) = 180^ Given m( ABC) = 60^ and m( ACB) = 40^: m( BAC) + 60^ + 40^ = 180^ m( BAC) + 100^ = 180^ m( BAC) = 180^ - 100^ m( BAC) = 80^ Step 2: Relate the inscribed angle BAC to the central angle BOC. The angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the remaining part of the circle. In this case, BOC is the central angle subtended by arc BC, and BAC is the inscribed angle subtended by the same arc BC. Therefore: m( BOC) = 2 × m( BAC) m( BOC) = 2 × 80^ m( BOC) = 160^ The final answer is 160^. That's 2 down. 3 left today — send the next one.