1. **State the problem:** We are given a circle with center O and points A, B, C, D, E on the circle. We need to find the measures of angles and arcs: m\angle A, mCE, m\angle C, m\angle D, and m\angle ABE. 2. **Given information:** - Arc BD = 74° - Angle at B = 24° - Arc AD = 84° 3. **Find m\angle A:** - Angle A is an inscribed angle that intercepts arc BD. - The measure of an inscribed angle is half the measure of its intercepted arc. 4. **Calculate m\angle A:** $$m\angle A = \frac{1}{2} \times m\overset{\frown}{BD} = \frac{1}{2} \times 74 = 37$$ **Final answer:** $$m\angle A = 37$$