Let's break down the syllogism step by step to reach the correct conclusion.
1. The first premise states:
"If a triangle is an obtuse triangle, then it has one obtuse angle."
- This tells us that an obtuse triangle always contains one obtuse angle (an angle greater than 90 degrees).
2. The second premise states:
"If a triangle has one obtuse angle, then the sum of the measures of the other two angles is less than 90 degrees."
- This implies that when a triangle has one angle that is greater than 90 degrees, the remaining two angles must add up to less than 90 degrees.
Combining these two premises, we can deduce the following:
- From the first premise, we know that an obtuse triangle has an obtuse angle.
- From the second premise, we know that if a triangle has an obtuse angle, the sum of the other two angles must be less than 90 degrees.
Therefore, logically, if a triangle is an obtuse triangle, then the sum of the measures of the other two angles is less than 90 degrees.
Hence, the correct completion of the syllogism is:
"If a triangle is an obtuse triangle, then the sum of the measures of the other two angles is less than 90 degrees."
The correct answer is:
O a triangle is an obtuse triangle, then the sum of the measures of the other two angles is less than 90 degrees.
