Which set of angles can form a triangle
The Correct Answer and Explanation is :
To determine which set of angles can form a triangle, we must remember two fundamental properties of triangle angles:
- The sum of the interior angles in any triangle must always equal (180^\circ).
- Each angle in a triangle must be greater than (0^\circ) (meaning no angle can be zero or negative).
Given these properties, we can analyze different sets of angles. Let’s say we have a set of angles: (30^\circ), (60^\circ), and (90^\circ).
Verification:
- Sum of Angles:
[
30^\circ + 60^\circ + 90^\circ = 180^\circ
]
This satisfies the first condition. - Individual Angles:
Each angle is greater than (0^\circ): - (30^\circ > 0^\circ)
- (60^\circ > 0^\circ)
- (90^\circ > 0^\circ)
Since both conditions are met, this set of angles can indeed form a triangle.
Alternative Examples:
- Set: (45^\circ), (45^\circ), and (90^\circ):
- Sum: (45^\circ + 45^\circ + 90^\circ = 180^\circ)
- Each angle is positive. This forms a right isosceles triangle.
- Set: (10^\circ), (20^\circ), and (150^\circ):
- Sum: (10^\circ + 20^\circ + 150^\circ = 180^\circ)
- Each angle is positive. This forms a scalene triangle.
- Set: (0^\circ), (60^\circ), and (120^\circ):
- Sum: (0^\circ + 60^\circ + 120^\circ = 180^\circ)
- However, one angle is (0^\circ), which violates the second condition. Thus, this set cannot form a triangle.
Conclusion:
Any set of three angles that sums to (180^\circ) and contains no angle less than or equal to (0^\circ) can form a triangle. Always check both conditions when determining if a set of angles can form a triangle.