Premises: If a triangle has an angle with a measure more than 90°, then the triangle is an obtuse triangle. The measure of an angle in △ABC is 110°. Conclusion: △ABC is an obtuse triangle. Is this law of syllogism or law of detachment?

we know that

Law of detachment is used when you have a conditional statement and another statement that matches the hypothesis of the conditional.

Law of syllogism is used when you have two conditionals and the hypothesis of one matches the conclusion of the other

in this problem we have the law of detachment

the conditional statement is

If a triangle has an angle with a measure more than 90°

the another statement that matches the hypothesis of the conditional

then the triangle is an obtuse triangle

therefore

the answer is

the law of detachment