Final answer:
To find the measure of angle ZQ, given that PQ is a tangent at Point P to Circle O with arc lengths of 160° and 60°, we use the fact that a tangent line is perpendicular to the radius to calculate the fourth angle in the quadrilateral. By subtracting the sum of the given angles from 360°, we determine that the measure of angle ZQ is 50°.
Step-by-step explanation:
The student's question is related to the properties of tangent lines and circle geometry. In the given problem, PQ is a tangent to Circle O at Point P, creating two arcs with measurements of 160° and 60°. To find the measure of angle ZQ, we can use the fact that a tangent line to a circle is perpendicular to the radius at the point of tangency. Since the sum of angles in a quadrilateral adds up to 360°, and we're given the other three angles (160°, 60°, and 90° for the right angle created by the tangent and radius), we can subtract the sum of these three angles from 360° to find the measure of angle ZQ.
Let's calculate the angle ZQ:
360° - (160° + 60° + 90°) = 360° - 310° = 50°
Therefore, the measure of angle ZQ is 50°.