Question
if a triangle has an angle of 22 and 46 what can be established about the third angle and what kind of triangle is it
Answers
GPT-4o mini
In a triangle, the sum of the interior angles is always 180 degrees. Given two angles of the triangle—22 degrees and 46 degrees—you can find the third angle by using the following formula:
\[
\text{Third angle} = 180 - (\text{First angle} + \text{Second angle})
\]
Substituting the given angles:
\[
\text{Third angle} = 180 - (22 + 46) = 180 - 68 = 112 \text{ degrees}
\]
So the third angle is 112 degrees.
Regarding the type of triangle, since one of the angles (112 degrees) is greater than 90 degrees, the triangle is classified as an obtuse triangle. An obtuse triangle has one angle that is greater than 90 degrees, while the other two angles are less than 90 degrees.
\[
\text{Third angle} = 180 - (\text{First angle} + \text{Second angle})
\]
Substituting the given angles:
\[
\text{Third angle} = 180 - (22 + 46) = 180 - 68 = 112 \text{ degrees}
\]
So the third angle is 112 degrees.
Regarding the type of triangle, since one of the angles (112 degrees) is greater than 90 degrees, the triangle is classified as an obtuse triangle. An obtuse triangle has one angle that is greater than 90 degrees, while the other two angles are less than 90 degrees.