Tree angles have the sizes 94°, 36.5°, and 49.5. Is it possible that these angles are in a triangle?
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Tree angles have the sizes 94°, 36.5°, and 49.5. 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 could be the values of angles in some triangle.
Possible.
Determine the size of angle ABC?
DBC = 100°
In mathematics, close isn't good enough - the sum must be exactly 180°. If you get 179.8° or 180.3°, those angles cannot form a triangle.
Absolutely! Angles can be any positive decimal value. What matters is that they're all less than 180° individually and sum to exactly 180° together.
No! The order doesn't matter for checking if angles can form a triangle. Whether you have 94°, 36.5°, 49.5° or 49.5°, 94°, 36.5°, the sum is still the same.
That's fine! Triangles can have obtuse angles (greater than 90°) as long as the total still equals 180°. In this problem, 94° makes it an obtuse triangle.
Line up the decimal points and add column by column:
94.0 + 36.5 + 49.5
Start with whole numbers (94 + 36 + 49 = 179), then decimals (0.0 + 0.5 + 0.5 = 1.0), giving 180.0°
Yes! Each individual angle must be greater than 0° and less than 180°. But the most important rule is that all three must sum to exactly 180°.
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