Three angles measure as follows: 60°, 50°, and 70°.
Is it possible that these are angles in a triangle?
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Three angles measure as follows: 60°, 50°, and 70°.
Is it possible that these are angles in a triangle?
Recall that the sum of angles in a triangle equals 180 degrees.
Let's add the three angles to see if their sum equals 180:
Therefore, it is possible that these are the values of angles in some triangle.
Possible.
Is the straight line in the figure the height of the triangle?
If the sum is greater than 180°, those angles cannot form a triangle. For example, 70° + 80° + 90° = 240°, which is impossible in any triangle.
If the sum is less than 180°, those angles also cannot form a triangle. The sum must be exactly 180° - no more, no less!
No! Two 90° angles already sum to 180°, leaving 0° for the third angle. Since angles must be greater than 0°, this is impossible.
Yes! Each angle must be greater than 0° and less than 180°. An angle of 0° or 180° would make the triangle collapse into a line.
Unfortunately, no reliable shortcut exists. You must add all three angles to verify they sum to exactly 180°. This is the fundamental rule that cannot be skipped!
That's fine! As long as the sum equals exactly 180.0°, the triangle is valid. For example: 60.5° + 59.2° + 60.3° = 180.0° ✓
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