Circle the angle(s) that could never be the smallest angle of a triangle.
8 degrees 47 degrees 88 degrees 91 degrees
47, 88, 91
I'm glad you think saucepans aren't for hinittg people some people would endeavor to disagree. By more punctuation I mean more periods, commas, etc., at the end of each bubble, yes. I don't really mind a lack of SFX translations, lol. I think my brain doesn't register reading them most of the time.
To determine the smallest angle of a triangle, we can use the fact that the sum of the angles in any triangle is always 180 degrees.
Let's test each angle option to see if it could be the smallest angle of a triangle:
1. 8 degrees: This angle could be the smallest angle of a triangle, as long as the other two angles add up to more than 172 degrees (180 - 8).
2. 47 degrees: This angle could also be the smallest angle of a triangle, as long as the other two angles add up to more than 133 degrees (180 - 47).
3. 88 degrees: This angle could be the smallest angle of a triangle, as long as the other two angles add up to more than 92 degrees (180 - 88).
4. 91 degrees: This angle could NOT be the smallest angle of a triangle, as the other two angles would have to add up to less than 89 degrees (180 - 91). But the smallest possible angle would be greater than 89 degrees, which violates the properties of a triangle.
Therefore, the angle that could never be the smallest angle of a triangle is 91 degrees.
To determine which angle could never be the smallest angle of a triangle, we need to recall the triangle inequality theorem, which states that the sum of any two angles in a triangle must be greater than the measure of the third angle. In other words, the smallest angle in a triangle must be smaller than the sum of the other two angles.
Let's apply this theorem to each angle given:
1. 8 degrees: To determine if this could be the smallest angle of a triangle, we need to consider the other two angles. Since both 47 degrees and 88 degrees are greater than 8 degrees, the sum of these two angles is definitely greater than 8 degrees. Therefore, 8 degrees could be the smallest angle of a triangle.
2. 47 degrees: Again, let's consider the other two angles. The first condition is already satisfied since 47 degrees is greater than 8 degrees. However, when we compare 47 degrees to 88 degrees, we see that it is smaller. In this case, the sum of 47 degrees and 88 degrees is greater than 91 degrees, and therefore, 47 degrees could indeed be the smallest angle of a triangle.
3. 88 degrees: Comparing 88 degrees to the other two angles, we can see that it is the largest among the given angles. Furthermore, the sum of 88 degrees and 8 degrees is still less than 91 degrees. Hence, 88 degrees could be the smallest angle of a triangle.
4. 91 degrees: Finally, let's examine the possibilities for 91 degrees. When we compare it to the other two angles, we observe that it is the largest angle. Moreover, the sum of 91 degrees and 8 degrees is still less than 88 degrees. Thus, 91 degrees could be the smallest angle of a triangle.
Therefore, none of the given angles could never be the smallest angle of a triangle, as they all satisfy the triangle inequality theorem.