Answer:
use the relations involving inscribed angles and external angles
Step-by-step explanation:
Call the measure of angle ABC by the name B. An inscribed angle (B) is half the measure of the arc it subtends. Then long arc AC is 2B, and short arc ABC is (360°-2B).
The external angle P, 36°, is half the difference of these values.
(2B -(360°-2B))/2 = 36°
2B - 180° = 36° . . . . . . . simplify
2B = 180° +36° = 216° . . . . add 180°
B = 108° . . . . . . . . . . . . . . . . . . divide by 2
m∠ABC = 108°
