Point A is on the inside of a maze that is a simple closed curve. A segment from point A to the outside of the maze must cross the border of the maze an ___EVEN____ number of times for point A to be inside the maze.
If a convex polyhedron has 6 vertices and 8 faces, then it has __12____ edges.
The number of points in a taxicab circle with radius 5 is ___20___.
Which of the following is the only degree measure that could not be the sum of the angle measures of a spherical triangle?
220°
300°
182°
544° <-----
See your original post.
To find out the degree measure that could not be the sum of the angle measures of a spherical triangle, we need to understand the properties of spherical triangles.
In a spherical triangle, the sum of its angle measures is always greater than 180 degrees and less than 540 degrees. This is because the total surface of a sphere is 4π steradians, which corresponds to 720 degrees in total. Since a spherical triangle occupies a portion of the sphere's surface, the sum of its angles cannot exceed 720 degrees.
Let's consider each option and check if it satisfies these conditions:
1. 220° - This can be a valid sum of angle measures of a spherical triangle since it is greater than 180 but less than 540 degrees.
2. 300° - Similarly, this can be a valid sum within the given range.
3. 182° - This can also be a valid sum.
4. 544° - Here, we see that the sum exceeds the upper limit of 540 degrees, making it impossible for a spherical triangle.
Therefore, the only degree measure that could not be the sum of the angle measures of a spherical triangle is 544°.