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 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 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 128°, and the triangle is an obtuse triangle.

Answer 1

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

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

You can calculate the third angle as follows:

\[
\text{Third angle} = 180° - (22° + 46°)
\]

\[
\text{Third angle} = 180° - 68°
\]

\[
\text{Third angle} = 112°
\]

Now, we can classify the triangle type:

- A triangle is classified as acute if all angles are less than 90°.
- A triangle is classified as right if one angle is exactly 90°.
- A triangle is classified as obtuse if one angle is greater than 90°.

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

Thus, the correct answer is:

"The third angle measure is 112°, and the triangle is an obtuse triangle."