Final answer:
To find the measure of arc AD, first determine the measure of the associated angles. Then, use the fact that the measure of an arc is twice the measure of its corresponding central angle to find the measure of arc AD.
Step-by-step explanation:
To find the measure of arc AD, we need to determine the measure of the angles associated with it. First, since segment BC is congruent to segment CD, we know that m∠BCD = m∠CBD. Since m∠BCD + m∠CBD + m∠ZBC = 180° (angle sum of a triangle), we can find m∠ZBC = 180° - m∠BCD - m∠CBD. Using the given information, we can substitute m∠BCD = 95° and m∠ZBC = 88° into the equation to find m∠CBD. Once we have m∠ZBC, m∠CBD, and m∠BCD, we can find m∠BAC using the fact that the angles in a triangle add up to 180°. Finally, to find the measure of arc AD, we use the fact that the measure of an arc is twice the measure of its corresponding central angle. So, m(arc AD) = 2 * m∠BAC.
By substituting the values we found into the equation, we can find the measure of arc AD.