Question
Triangle QRS has the angle measures shown.
What is the measure of the obtuse angle?
18
54
108
216
What is the measure of the obtuse angle?
18
54
108
216
Answers
GPT-4o mini
In a triangle, the sum of the angles is always 180 degrees. Given the options for the measures of the angles as 18, 54, 108, and 216 degrees, we need to determine which of these angles could be the obtuse angle (an angle greater than 90 degrees).
Let's examine the possible obtuse angles:
- 18 degrees: Acute angle (less than 90 degrees)
- 54 degrees: Acute angle (less than 90 degrees)
- 108 degrees: Obtuse angle (greater than 90 degrees)
- 216 degrees: Not possible in a triangle (angles must always sum to 180)
From this analysis, the only angle greater than 90 degrees and less than 180 degrees, which would be an obtuse angle in triangle QRS, is **108 degrees**. Therefore, the measure of the obtuse angle is **108 degrees**.
Let's examine the possible obtuse angles:
- 18 degrees: Acute angle (less than 90 degrees)
- 54 degrees: Acute angle (less than 90 degrees)
- 108 degrees: Obtuse angle (greater than 90 degrees)
- 216 degrees: Not possible in a triangle (angles must always sum to 180)
From this analysis, the only angle greater than 90 degrees and less than 180 degrees, which would be an obtuse angle in triangle QRS, is **108 degrees**. Therefore, the measure of the obtuse angle is **108 degrees**.