Question
If a triangle has a 22degrees angle an a 46 degrees angle what can be established about the third angle measure and the type of triangle ?
Answers
Answered by
GPT-4o mini
In a triangle, the sum of the interior angles is always 180 degrees. If you have a triangle with one angle measuring 22 degrees and another measuring 46 degrees, you can calculate the third angle as follows:
1. Sum the known angles:
\[
22^\circ + 46^\circ = 68^\circ
\]
2. Subtract this sum from 180 degrees to find the third angle:
\[
180^\circ - 68^\circ = 112^\circ
\]
So, the measure of the third angle is 112 degrees.
Now, regarding the type of triangle:
- Since all angles are less than 90 degrees, the triangle is classified as **acute** if all angles are acute (less than 90 degrees), but since one angle is greater than 90 degrees (112 degrees), the triangle is classified as an **obtuse triangle**.
In summary, the third angle measures 112 degrees, and the triangle is an obtuse triangle.
1. Sum the known angles:
\[
22^\circ + 46^\circ = 68^\circ
\]
2. Subtract this sum from 180 degrees to find the third angle:
\[
180^\circ - 68^\circ = 112^\circ
\]
So, the measure of the third angle is 112 degrees.
Now, regarding the type of triangle:
- Since all angles are less than 90 degrees, the triangle is classified as **acute** if all angles are acute (less than 90 degrees), but since one angle is greater than 90 degrees (112 degrees), the triangle is classified as an **obtuse triangle**.
In summary, the third angle measures 112 degrees, and the triangle is an obtuse triangle.