Let's start by looking at the angles of the given triangle as labeled by Curtis.
His friend Arnoldo says that at least one of his measures is incorrect. We want to find two different ways to explain why Arnoldo knows that this is true.
Since the measurements do not add up to 180^(∘), they cannot all be correct.
Second Explanation
Let's classify the angles of the triangle according to Curtis's measures.
Angle Measure
Classification
Reason
37
Acute
0<37<90
93
Obtuse
90<93<180
130
Obtuse
90<130<180
According to Corollary 4.2 of the Triangle Angle-Sum Theorem, there can only be at most one obtuse angle in any given triangle. Since there are two obtuse angle measures among Curtis's measurements, they cannot be both correct.
Extra
Types of Angles
Angles can be classified by their measures. For angles between 0^(∘) and 180^(∘), they can be divided into four categories: acute, right, obtuse, and straight.
Acute angle &: measures less than 90 ^(∘)
Right angle &: measures exactly 90 ^(∘)
Obtuse angle &: measures greater than 90 ^(∘)
Straight angle &: measures exactly 180 ^(∘)
