Answer:
x = 25
Step-by-step explanation:
The measure of an inscribed angle in a circle is half the measure of the arc it subtends. The acute angles in a right triangle are complementary.
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Inscribed angle CAD is half the measure of arc CD, so is 80°/2 = 40°.
Acute angle 2x° is the complement of angle CAD in the right triangle shown, so we have ...
2x° = 90° -40° = 50°
x = 25 . . . . . . . . . . . . divide by 2°
