Answer:
arc BC = 26°
arc AB = 90°
arc CAB = 334°
Step-by-step explanation:
The angles of a linear pair total 180°. This fact lets us write an equation for x that helps us find the measures of all the angles and arcs. The arcs of a circle total 360°.
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equation
∠APE +∠EPD = 180°
(25x +15)° +(33x -9)° = 180°
58x = 174 . . . . . . divide by °, subtract 6
x = 3 . . . . . . . . divide by 58
angles
Angle APE is ...
∠APE = (25x +15)° = (25·3 +15)° = 90°
Then ...
∠EPD = 180° -90° = 90°
∠DPC = (20·3 +4)° = 64°
∠CPB = 90° -64° = 26°
arcs
arc BC = ∠BPC = 26°
arc AB = ∠APB = 180° -90° = 90°
arc CAB = 360° -arc AB = 334°
