Question
If a triangle has a 22° angle and a 46° angle, what can be established about the third angle measure and the type of triangle?
Answers
GPT 3.5
To find the measure of the third angle in the triangle, we can subtract the sum of the given angles from 180°, since the sum of the angles in any triangle is always 180°.
So, the measure of the third angle is:
180° - (22° + 46°) = 180° - 68° = 112°
Therefore, the measure of the third angle is 112°.
Now, let's analyze the type of triangle based on the measures of its angles:
- If all three angles are less than 90°, it is an acute triangle.
- If one angle is exactly 90°, it is a right triangle.
- If one angle is greater than 90°, it is an obtuse triangle.
Since none of the angles in this triangle are 90° or greater, the triangle is an acute triangle.
So, the measure of the third angle is:
180° - (22° + 46°) = 180° - 68° = 112°
Therefore, the measure of the third angle is 112°.
Now, let's analyze the type of triangle based on the measures of its angles:
- If all three angles are less than 90°, it is an acute triangle.
- If one angle is exactly 90°, it is a right triangle.
- If one angle is greater than 90°, it is an obtuse triangle.
Since none of the angles in this triangle are 90° or greater, the triangle is an acute triangle.