Multiple choice

A square ABCD is inscribed in a circle. There is a point E on minor arc AB. Find the measure of angle AEB (in degrees)?

  1. 90

  2. 105

  3. 120

  4. 135
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D Correct answer
Explanation

In a cyclic quadrilateral ABCD (square), angle AEB + angle ACB = 180. Angle ACB is 45 degrees (diagonal of square). So angle AEB = 180 - 45 = 135 degrees.

AI explanation

Since the square ABCD is inscribed in the circle, diagonal AC is the diameter. The angle AEB is an angle formed in the opposite arc, specifically the major arc AB, by point E on the minor arc AB. The arc AB measures 90 degrees, so the reflex angle AEB intercepts 270 degrees, making angle AEB half of 270 degrees, which is 135 degrees.

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