1. **State the problem:** We are given a circle with center O and points A, B, C, D, and 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:** - m\angle A = 37 (already given) - Arcs with measures 72°, 24°, and 84° are visible. 3. **Recall important rules:** - The measure of an inscribed angle is half the measure of its intercepted arc. - The measure of an arc is the sum of the measures of the arcs it contains. - Vertical angles formed by intersecting chords are equal. 4. **Find mCE:** - Arc CE is the sum of arcs C to E. - Given arcs 72°, 24°, and 84°, identify which arcs correspond to CE. - Assuming arc CE = 72° + 24° = 96°. 5. **Find m\angle C:** - Angle C intercepts arc AE. - Arc AE = 84° + 24° = 108°. - So, m\angle C = \frac{1}{2} \times 108 = 54. 6. **Find m\angle D:** - Angle D intercepts arc BE. - Arc BE = 72° + 84° = 156°. - So, m\angle D = \frac{1}{2} \times 156 = 78. 7. **Find m\angle ABE:** - Angle ABE intercepts arc AE. - Arc AE = 84° + 24° = 108°. - So, m\angle ABE = \frac{1}{2} \times 108 = 54. **Final answers:** - a. m\angle A = 37 - b. mCE = 96 - c. m\angle C = 54 - d. m\angle D = 78 - e. m\angle ABE = 54