Answer:
E. 26.25°
Explanation:
Given a diagram showing an angle at crossed chords of 2x, you want the value of x/2.
Inscribed angle
The measure of an inscribed angle is half the measure of the arc it subtends. This means the triangle interior angle at upper left has half the measure of the 40° arc it subtends: 20°.
Angle sum
The sum of angles in the triangle is 180°. The third angle is a vertical angle to the one marked 2x, so has that same measure. Then the relation is ...
2x +20° +55° = 180°
2x = 105° . . . . . . . . . . . . . subtract 75°
x/2 = 26.25° . . . . . . . . . divide by 4
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Additional comment
You can apply a "reasonableness" test to the answer choices. Any angle where lines cross cannot have a measure more than 180°. If that angle is 2x, then x/2 cannot be more than 180°/4 = 45°. Only one answer choice is less than 45°.