Possible measures of three angles of a triangle are

Options

A. `33^@, 42^@, 115^@`
B. `40^@, 70^@, 80^@`
C. `30^@, 60^@, 100^@`
D. `50^@, 60^@, 70^@`

Answer

To determine the possible measures of three angles of a triangle, we need to remember that the sum of the angles in a triangle is always 180 degrees. We will evaluate given sets of angles to see if they meet this criterion.

### Step-by-Step Solution:

1. **Understand the Triangle Angle Sum Property**:
- The sum of the three angles in a triangle must equal 180 degrees.

2. **Evaluate the First Set of Angles (50°, 60°, 70°)**:
- Calculate the sum:
\[ 50 + 60 + 70 = 180 \]
- Since the sum is 180 degrees, this set is a possible measure of angles for a triangle.

3. **Evaluate the Second Set of Angles (100°, 60°, 30°)**:
- Calculate the sum:
\[ 100 + 60 + 30 = 190 \]
- Since the sum exceeds 180 degrees, this set is NOT a possible measure of angles for a triangle.

4. **Evaluate the Third Set of Angles (40°, 70°, 80°)**:
- Calculate the sum:
\[ 40 + 70 + 80 = 190 \]
- Again, since the sum exceeds 180 degrees, this set is NOT a possible measure of angles for a triangle.

5. **Evaluate the Fourth Set of Angles (42°, 33°, 75°)**:
- Calculate the sum:
\[ 42 + 33 + 75 = 150 \]
- Since the sum is less than 180 degrees, this set is NOT a possible measure of angles for a triangle.

6. **Conclusion**:
- The only valid set of angles that can form a triangle is (50°, 60°, 70°).

### Final Answer:
The possible measures of three angles of a triangle are 50°, 60°, and 70°.