Question

A triangle has angles A, B, and C. Which of the following could not be a set of angles?

A. ∠A = 100°, ∠B = 50°, ∠C = 30°
B. ∠A = 91°, ∠B = 47°, ∠C = 42°
C. ∠A = 101°, ∠B = 49°, ∠C = 39°
D. ∠A = 90°, ∠B = 45°, ∠C = 45°

Answer 1

Option C (°A = 101°, °B = 49°, °C = 39°) is the set of angles that could not form a triangle, as their sum of 189° exceeds the required 180° for a triangle.

Step-by-step explanation:

We need to determine which set of angles cannot represent the angles of a triangle. The fundamental rule is that the sum of the angles in a triangle must be exactly 180°. Now let's examine the given sets of angles:

• °A = 100°, °B = 50°, °C = 30°. The sum is 100 + 50 + 30 = 180°, which is correct for a triangle.
• °A = 91°, °B = 47°, °C = 42°. The sum is 91 + 47 + 42 = 180°, again correct.
• °A = 101°, °B = 49°, °C = 39°. The sum is 101 + 49 + 39 = 189°. This sum is more than 180°, so this set of angles cannot form a triangle.
• °A = 90°, °B = 45°, °C = 45°. The sum is 90 + 45 + 45 = 180°, which is valid for a triangle.

Therefore, the set of angles that could not form a triangle is Option C: °A = 101°, °B = 49°, °C = 39°, because their sum exceeds 180°.