Question

Aliaa uses deductive reasoning to identify the number angles that fit inside a circle based on her knowledge that obtuse angles have measures greater than  and that there are  at the center of the circle. Aliaa wants to partition the circle in 3 congruent angles, what is the angle measurement that best fits Aliaa's circle partition?

Answer 1

The best angle measurement that best fits Aliaa's circle partition is three angles of 120° each.

Explanation:

The sum of angles at the center of the circle = The sum of angles at a point = 360°

Therefore, to partition the circle into three congruent angles, the measurement of each of the partition should be 360°/3 = 120°

The steps to partition a circle into three are;

1) Draw the diameter of the circle, to intersect the circumference of the circle at points A and B

2) Mark a point, C, at a distance of half the radius from the center of the circle, O, to the point, B, on the circumference, using a straight edge

3) Draw a perpendicular line to the diameter of the circle, through the point, C, to intersect the circle circumference at points D and E)

4) Draw radial lines from the circle center, O, to the points D and E

5) The segments OA, OB, and OE, are segment lines partitioning the segment into three congruent angles.