Tree angles have the sizes:
31°, 122°, and 85.
Is it possible that these angles are in a triangle?
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Tree angles have the sizes:
31°, 122°, and 85.
Is it possible that these angles are in a triangle?
Let's remember that the sum of angles in a triangle is equal to 180 degrees.
We'll add the three angles to see if their sum equals 180:
Therefore, these cannot be the values of angles in any triangle.
Impossible.
Is DE side in one of the triangles?
This is a fundamental property of triangles in flat geometry! No matter what type of triangle - big, small, acute, or obtuse - the three interior angles always sum to 180°.
In math problems, the sum must be exactly 180°. In real measurements, small differences might be due to rounding, but for theoretical problems, anything other than 180° means no triangle exists.
Yes! Obtuse triangles have one angle greater than 90°. But since all three angles must still sum to 180°, the other two angles must be quite small to compensate.
Look for warning signs: If you see an angle close to or over 120°, be suspicious! Also, if two angles already add up to more than 120°, the third would need to be negative.
Just under 180°! As one angle approaches 180°, the other two must approach 0°, making the triangle extremely flat. In practice, angles are usually much smaller.
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