The chord AB divides the circle with the center O into two arcs. Determine the degree measure of the central angle

| March 8, 2021 | education

The chord AB divides the circle with the center O into two arcs. Determine the degree measure of the central angle corresponding to the arc AB, if the ratio of the degree measures of the arcs is …

We denote the degree measure of the smaller arc AB through 2 * X0, then the large arc AB is equal to 7 * X0.

The degree measure of a full circle is 360, then (2 * X + 7 * X) = 360.

9 * X = 360.

X = 360/9 = 40.

Then the degree measure of the smaller arc AB = 2 * 40 = 80.

The central angle of the AOB is equal to the degree measure of the arc on which it rests. Angle AOB = 80.

Similarly:

3 * X + 5 * X = 360.

8 * X = 360.

X = 360/8 = 45.

Arc AB = 3 * 45 = 135.

Angle AOB = 135.

7 * X + 11 * X = 360.

18 * X = 360.

X = 360/18 = 20.

Arc AB = 7 * 20 = 140.

Angle AOB = 140.

Answer: Angle AOB is equal to: a) 80, b) 135, c) 140.



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