Tree angles have the sizes:
76°, 52°, and 52°.
Is it possible that these angles are in a triangle?
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Tree angles have the sizes:
76°, 52°, and 52°.
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 will add the three angles to find out if their sum equals 180:
Therefore, these could be the values of angles in some triangle.
Yes.
Determine the size of angle ABC?
DBC = 100°
Then those angles cannot form a triangle! For example, if you had 90°, 60°, and 40°, the sum would be 190°, which is impossible for a triangle.
Yes! This creates an isosceles triangle, which has two equal angles and two equal sides. It's perfectly valid as long as all three angles sum to 180°.
This is a fundamental property of triangles in flat (Euclidean) geometry. You can prove it by extending one side and using the fact that angles on a straight line sum to 180°.
Less than 180°! If one angle were 180° or more, the other two angles would have to be zero or negative, which is impossible. The largest possible angle approaches (but never reaches) 180°.
Think "Triangle = 180"! Draw a quick triangle on your paper and write 180° next to it as a reminder. This visual cue helps prevent careless mistakes.
That's fine! Angles can be measured in decimals or fractions. Just make sure your final sum equals exactly (accounting for any rounding).
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