P is a point that is not on line m. How many lines can be drawn through P that form a 30 degree angle with line m?
Only one line.
To find the number of lines that can be drawn through point P that form a 30-degree angle with line m, we need to consider the properties of angles and lines.
1. Start by drawing line m and point P on a piece of paper or a computer sketch tool.
2. Since the angle formed by the line through P and line m is 30 degrees, we know that there are two possible angles (each measuring 30 degrees) that can be formed on either side of line m.
3. However, we also know that for any given point not on a line, there is only one line that can be drawn parallel to that line.
4. So, drawing one line that forms a 30-degree angle with line m creates another angle measuring 150 degrees on the opposite side. These two angles are supplementary (add up to 180 degrees).
5. Therefore, only one line can be drawn through point P that forms a 30-degree angle with line m.
In conclusion, only one line can be drawn through point P to form a 30-degree angle with line m.