using two triangle rulers with angles of (30, 60, 90) and (45 , 45, 90) how many angles less than 180 degrees can be drawn?
mmmh???
I could do a
30°, 45°, 60° , 90° , 75°, 105°, 120°, 135°, 150°, 165°
Can you see any I missed ?
That would be 145 degrees.
11 combinations in total! Thanks for your help Reiny, I appreciate it.
How would you get 145°
Mistaken, I did 30 + 105 and thought it was 145 :P thanks for your help though.
There are actually more than what I gave you.
Mine are only from the addition of these angles.
How about subtractions ?
e.g. 45 - 30 = 15
Can you find some more?
You are a genius! 15 is the last one.
To determine how many angles less than 180 degrees can be drawn using the two given triangle rulers, we need to consider the possible combinations of angles from both rulers.
First, let's list the angles of the two triangle rulers:
Triangle Ruler 1: 30°, 60°, 90°
Triangle Ruler 2: 45°, 45°, 90°
Now, let's examine the possible combinations of angles:
1. Using Triangle Ruler 1: We can draw a triangle with any combination of its angles. Since all angles are less than 180 degrees, we have three possibilities: 30°, 60°, and 90°.
2. Using Triangle Ruler 2: Again, we can draw a triangle with any combination of its angles. So, we have two possibilities: two angles of 45° each, or the right angle of 90°.
Now, let's combine the two triangle rulers and consider the possibilities:
- Combining a triangle with 30° and 45° angles: This will result in a triangle with angles of 30°, 45°, and 105° (30° + 45° = 75°, subtracting from 180).
- Combining a triangle with 30° and 90° angles: This will result in a triangle with angles of 30°, 90°, and 60° (30° + 90° = 120°, subtracting from 180).
- Combining a triangle with 60° and 45° angles: This will result in a triangle with angles of 60°, 45°, and 75° (60° + 45° = 105°, subtracting from 180).
- Combining a triangle with 60° and 90° angles: This will result in a triangle with angles of 60°, 90°, and 30° (60° + 90° = 150°, subtracting from 180).
- Combining a triangle with 90° and 45° angles: This will result in a triangle with angles of 90°, 45°, and 45°.
Combining the angles from both triangle rulers allows us to form five additional triangles with angles less than 180 degrees.
Therefore, in total, we can draw eight triangles with angles less than 180 degrees using the two given triangle rulers.