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.
Determine the size of angle ABC?
DBC = 100°
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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