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 128°
, and the triangle is an obtuse triangle.
The third angle measure is 128 degrees , and the triangle is an obtuse triangle.

The third angle measure is 68°
, and the triangle is an obtuse triangle.

Answer 1

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

In this case, you have:

1. First angle = 22°
2. Second angle = 46°

Now, we can calculate the third angle:

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

So, the third angle measure is 112°.

Next, to determine the type of triangle based on the angles:
- An acute triangle has all angles less than 90°.
- A right triangle has one angle that is exactly 90°.
- An obtuse triangle has one angle that is greater than 90°.

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

Therefore, the correct response is:

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