Multiple choice

In a circle of radius 6 cm, arc AB makes an angle of 114° with centre of the circle O. What is angle ABO?

  1. 23°

  2. 42°

  3. 38°

  4. 33°
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In triangle OAB, OA = OB = radius = 6 cm. Thus, it is an isosceles triangle. The base angles OAB and OBA are equal. The sum of angles is 180. Angle OAB + Angle OBA + Angle AOB = 180. 2 * Angle ABO + 114 = 180. 2 * Angle ABO = 66. Angle ABO = 33 degrees.

AI explanation

In triangle AOB, the radii OA and OB are equal in length, making it an isosceles triangle with angle OAB equal to angle OBA. Because the sum of angles in a triangle is 180 degrees, we have angle OAB + angle OBA + 114 = 180. Substituting angle OAB with angle OBA gives 2 times angle OBA = 66, so angle OBA is 33 degrees. The measure of angle ABO is 33 degrees.

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