Based on the triangle sum theorem and the triangle inequality theorem:
1. B. 23°, 67°, 90°.
2. A. 1 cm, 2 cm, 3 cm.
What is the Triangle Sum Theorem?
According to the triangle sum theorem, all three interior angles of any triangle has a sum of 180 degrees.
What is the Triangle Inequality Theorem?
Based on the triangle inequality theorem, one side of a triangle must be less than or equals the sum of any other two sides of the triangle. (a + b ≥ c).
Part 1:
23° + 67° + 90° = 180°, therefore, based on the triangle sum theorem, the set of angle measures that could be the interior angles of a triangle is: B. 23°, 67°, 90°.
Part 2:
1 + 2 = 3
1 + 3 > 2
2 + 3 > 1
Therefore, based on the triangle inequality theorem, the set of side lengths that could be that of the sides of a triangle is: A. 1 cm, 2 cm, 3 cm.
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