Question

yolanda has divided a circular apple pie into 4 slices by cutting the pie along 4 radii. The central angles of the 4 slices are 3x, 6x - 10, 4x + 10, and 5x degrees. What exactly are the numerical measures of the central angles?

Answer 1

Answer:

The numerical measures of the central angles are 60°, 110°, 90° and 100°

Step-by-step explanation:

It is given that, yolanda has divided a circular apple pie into 4 slices by cutting the pie along 4 radii. The central angles of the 4 slices are 3x, 6x - 10, 4x + 10, and 5x degrees

To find the value of x

The central angle is 360°

The four central angles are,3x, 6x - 10, 4x + 10, and 5x

Therefore we can write,

3x + (6x -10) + (4x - 10) + 5x = 360

3x + 6x - 10 + 4x - 10 + 5x = 360

3x + 6x + 4x + 5x  - 10 + 10 = 360

18x = 360

18x = 360

x = 360/18 = 20

Therefore the value of x = 20

To find each angles

3x = 3 * 20 = 60°

6x - 10 = 6 * 20 - 10 = 110°

4x + 10 = 4*20 + 10 = 90°

5x = 5 * 20 = 100°

Therefore the angles are, 60°, 110°, 90° and 100°