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
ophexymwandira1, let's knock this out. Step 1: Apply the Alternate Segment Theorem. The angle between a tangent (FE) and a chord (CD) at the point of contact (C) is equal to the angle in the alternate segment. Given DCE = 30^. Therefore, the angle subtended by chord CD in the alternate segment, CAD, is equal to DCE. CAD = DCE = 30^ Step 2: Find BAC. We are given BAD = 70^. From the figure, BAD is composed of BAC and CAD. BAD = BAC + CAD Substitute the known values: 70^ = BAC + 30^ Solve for BAC: BAC = 70^ - 30^ BAC = 40^ Step 3: Apply the Angle at the Centre Theorem. The angle subtended by an arc (BC) at the centre (O) is twice the angle subtended by the same arc at any point on the remaining part of the circumference (A). BOC = 2 × BAC Substitute the value of BAC: BOC = 2 × 40^ BOC = 80^ The angle 80^ is an acute angle. The size of the acute angle BOC is 80^. Got more? Send 'em