Final answer:
The given angles 5 2/3°, 64 1/3°, and 87° do not form a triangle since their sum is not 180°. The first angle should be adjusted to 28.67° for the measures to form a valid triangle.
Step-by-step explanation:
The question is about determining if the given angle measures can form a triangle and, if not, adjusting one of the angles to make the measures valid for a triangle. A key concept here is that the sum of the interior angles of a triangle always equals 180 degrees. Using this concept, we sum the given angles: 5 2/3°, 64 1/3°, and 87° to check if their total equals 180°. After converting the fractions, we have:
- 5 2/3° = 5 + 2/3 = 5.67°
- 64 1/3° = 64 + 1/3 = 64.33°
Adding them together with 87°:
5.67° + 64.33° + 87° = 157°
This sum does not equal 180°; hence, these angle measures cannot form a triangle. To correct the first angle so that the angles form a triangle, we need to find a new value such that the sum of all three angles is 180°.
Let x be the new value for the first angle. Then:
x + 64.33° + 87° = 180°
x = 180° - (64.33° + 87°)
x = 180° - 151.33°
x = 28.67°
Therefore, to have a valid set of angle measures for a triangle, the first angle should be adjusted to 28.67°.