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?

Answer 1

The sum of the angles in a triangle is always 180°. Thus, if a triangle has a 22° angle and a 46° angle, the third angle can be found by subtracting the sum of these two angles from 180°:

Third angle = 180° - (22° + 46°) = 180° - 68° = 112°

Therefore, the third angle measure is 112°.

As for the type of triangle, we can analyze based on the angle measures:
- If all three angles are less than 90°, the triangle is acute.
- If one angle is exactly 90°, the triangle is right.
- If one angle is greater than 90°, the triangle is obtuse.

Since all three angles in this case are less than 90° (22°, 46°, and 112°), we can conclude that the triangle is an acute triangle.