Question
If one interior angle of a triangle measure 73°, which set of remaining angles could not be the other two interior angles Of that triangle
73 and 34
106 and one
97 and 50
25 and 82
73 and 34
106 and one
97 and 50
25 and 82
Answers
GPT-4o mini
In a triangle, the sum of the interior angles must equal 180 degrees. Given one angle of 73°, we can find the sum of the other two angles:
\[
\text{Sum of the other two angles} = 180° - 73° = 107°
\]
Now, we'll evaluate each option to see if the two angles in each set add up to 107°.
1. **73 and 34**:
\[
73 + 34 = 107° \quad \text{(valid)}
\]
2. **106 and one**:
We cannot determine 'one', but if we interpret it as '1', then:
\[
106 + 1 = 107° \quad \text{(valid)}
\]
But 'one' is unclear. Assuming it means 1, it's valid. If it was meant to be something else, we need clarity.
3. **97 and 50**:
\[
97 + 50 = 147° \quad \text{(not valid)}
\]
4. **25 and 82**:
\[
25 + 82 = 107° \quad \text{(valid)}
\]
Based on this analysis, the set of angles that could NOT be the other two interior angles of the triangle is **97 and 50** since they sum to 147°, which exceeds 180°.
\[
\text{Sum of the other two angles} = 180° - 73° = 107°
\]
Now, we'll evaluate each option to see if the two angles in each set add up to 107°.
1. **73 and 34**:
\[
73 + 34 = 107° \quad \text{(valid)}
\]
2. **106 and one**:
We cannot determine 'one', but if we interpret it as '1', then:
\[
106 + 1 = 107° \quad \text{(valid)}
\]
But 'one' is unclear. Assuming it means 1, it's valid. If it was meant to be something else, we need clarity.
3. **97 and 50**:
\[
97 + 50 = 147° \quad \text{(not valid)}
\]
4. **25 and 82**:
\[
25 + 82 = 107° \quad \text{(valid)}
\]
Based on this analysis, the set of angles that could NOT be the other two interior angles of the triangle is **97 and 50** since they sum to 147°, which exceeds 180°.