If a triangle has a 22°

Question

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 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 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.

Answer 1

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

Given angles:

• First angle = 22°
• Second angle = 46°

We can find the third angle (let's call it \( x \)) with the following equation:

\[ x = 180° - (22° + 46°) = 180° - 68° = 112° \]

Now, let's classify the triangle based on the angle measures:

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

In this case, the third angle is 112°, which is greater than 90°. Therefore, the triangle is an obtuse triangle.

So, the correct response is:

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