The measure of arc AB is 38⁰. (Option A)
The measure of arc AEC is 142⁰. (Option A).
How to calculate the measure of the missing angles?
The measure of the missing angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Let the center of the circle = O
m∠AOB = 180 - (90 + 52) (sum of angles on a straight line)
m∠AOB = 38⁰
The measure of arc AB is calculated as;
arc AB = m∠AOB (intersecting chords at the center)
arc AB = 38⁰
The measure of arc AEC is calculated as follows;
arc AEC = m∠ACE (intersecting chords at the center)
m∠ACE = 180 - 38 (sum of angles on a straight line)
m∠ACE = 142⁰
arc AEC = 142⁰