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°
