To classify the triangle that Kevin drew with angle measures of 30° and 40° and side lengths of 5 cm, 7 cm, and 8 cm, we will analyze the angles and the lengths of the sides.
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Sum of Angles: First, let's calculate the third angle of the triangle. The sum of all angles in a triangle is always 180°.
\[ \text{Third angle} = 180° - (30° + 40°) = 180° - 70° = 110° \]
So, the angles of the triangle are 30°, 40°, and 110°.
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Type of Triangle by Angles:
- Since one of the angles (110°) is greater than 90°, this triangle is classified as an obtuse triangle.
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Lengths of Sides: We now look at the sides:
- The side lengths are 5 cm, 7 cm, and 8 cm.
- To classify the triangle based on side lengths, we can check whether all sides are of different lengths:
- Since 5 cm, 7 cm, and 8 cm are all different, this triangle is also classified as a scalene triangle (where all sides have different lengths).
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Conclusion: Thus, the triangle that Kevin drew is an obtuse scalene triangle because it has one obtuse angle (greater than 90°) and all sides of different lengths.
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