Which set of angles can be used to construct a triangle?
A. 88°, 34°, and 58°
B. 72°, 73°, and 54°
C. 89°, 46°, and 54°
D. 95°, 50°, and 27°
B. 72°, 73°, and 54°
Wrong.
I apologize for the mistake. The correct answer is option C. 89°, 46°, and 54°.
To construct a triangle, the sum of any two angles must be greater than the third angle.
In option A, 88° + 34° = 122° which is not greater than 58°. Therefore, these angles cannot form a triangle.
In option B, 72° + 73° = 145° which is greater than 54°. However, 72° + 54° = 126° which is not greater than 73°. Therefore, these angles cannot form a triangle.
In option C, 89° + 46° = 135° which is greater than 54°. Also, 46° + 54° = 100° which is greater than 89°. Therefore, these angles can form a triangle.
In option D, 95° + 50° = 145° which is greater than 27°. However, 50° + 27° = 77° which is not greater than 95°. Therefore, these angles cannot form a triangle.
To determine which set of angles can be used to construct a triangle, we need to check if the sum of the angles in each set is equal to 180°.
Let's calculate the sums for each option:
A. 88° + 34° + 58° = 180° (This set can be used to construct a triangle.)
B. 72° + 73° + 54° = 199° (This set cannot be used to construct a triangle, as the sum is greater than 180°.)
C. 89° + 46° + 54° = 189° (This set cannot be used to construct a triangle, as the sum is greater than 180°.)
D. 95° + 50° + 27° = 172° (This set cannot be used to construct a triangle, as the sum is less than 180°.)
Therefore, the correct answer is A. 88°, 34°, and 58°, as these angles add up to 180°, which satisfies the condition for constructing a triangle.