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
Step 1: Identify the properties of tangents and radii. Given that TP and TQ are tangents to a circle with center O, the radii OP and OQ are perpendicular to the tangents at the points of tangency P and Q, respectively. Therefore, we have: OPT = 90^ OQT = 90^ Step 2: Use the sum of angles in a quadrilateral. The points O, P, T, and Q form a quadrilateral OPTQ. The sum of the interior angles of a quadrilateral is 360^. So, we can write the equation: OPT + PTQ + OQT + POQ = 360^ Step 3: Substitute the known values into the equation. We are given POQ = 110^. Substituting the known angles: 90^ + PTQ + 90^ + 110^ = 360^ Step 4: Solve for PTQ. Combine the constant terms: 290^ + PTQ = 360^ Subtract 290^ from both sides: PTQ = 360^ - 290^ PTQ = 70^ The value of PTQ is 70^.