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?(1 point) Responses The third angle measure is 112° , and the triangle is an acute triangle. The third angle measure is 112 degrees , and the triangle is an acute triangle. The third angle measure is 112° , and the triangle is an obtuse triangle. The third angle measure is 112 degrees , and the triangle is an obtuse triangle. The third angle measure is 68° , and the triangle is an obtuse triangle. The third angle measure is 68 degrees , and the triangle is an obtuse triangle. The third angle measure is 128° , and the triangle is an obtuse triangle.

Answer 1

To find the third angle of a triangle when two angles are known, you can use the fact that the sum of the angles in a triangle is always 180°.

Given:
- First angle = 22°
- Second angle = 46°

Calculate the third angle:
\[
\text{Third angle} = 180° - (22° + 46°) = 180° - 68° = 112°
\]

Now, looking at the type of triangle:
- An acute triangle has all angles less than 90°.
- A right triangle has one angle equal to 90°.
- An obtuse triangle has one angle greater than 90°.

Since the third angle is 112°, which is greater than 90°, the triangle is an obtuse triangle.

Therefore, the correct response is:
**The third angle measure is 112°, and the triangle is an obtuse triangle.**