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 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 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 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 all three angles in a triangle equals 180°.

Given the angles of 22° and 46°, we can calculate the third angle as follows:

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

Calculating it:

\[ \text{Third Angle} = 180° - 68° = 112° \]

Now, we can determine the type of triangle based on its angles. A triangle is considered obtuse if one of its angles is greater than 90°. Since the third angle measures 112°, which is greater than 90°, the triangle is indeed an obtuse triangle.

Therefore, the correct response is:

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