a triangle has a 22°

Question

22
°
angle and a 46°
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°
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°
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°
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°
112
°
, and the triangle is an obtuse triangle.

Answer 1

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

Given angles:

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

We can find the third angle by calculating:

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

First, add the two known angles:

\[ 22° + 46° = 68° \]

Now, subtract this sum from 180°:

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

The third angle measure is 112°. Since all angles in this triangle (22°, 46°, and 112°) are less than 180°, and one angle (112°) is greater than 90°, this triangle is classified as an obtuse triangle.

Thus, the correct response is:

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