4. Find ∠ABE.

Let's analyze the geometry problem step by step. 1. Understanding the given information: * ∠BAE = 20° * ∠APE = 50° 2. Key Observations: * ∠APE is an inscribed angle that intercepts arc AE. * The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, arc AE = 2 * ∠APE = 2 * 50° = 100°. * ∠ABE is also an inscribed angle intercepting arc AE. 3. Finding ∠ABE: * Since ∠ABE intercepts arc AE, its measure is half the measure of arc AE. * ∠ABE = (1/2) * arc AE = (1/2) * 100° = 50°. Therefore, the measure of angle ABE is 50 degrees. Answer: 50°