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 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 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 obtuse triangle.
The third angle measure is  112 degrees , 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 any triangle is \(180^\circ\).

Given the angles \(22^\circ\) and \(46^\circ\):

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

So, the measure of the third angle is \(112^\circ\).

Since one of the angles (112°) is greater than \(90^\circ\), this means that the triangle is an obtuse triangle.

Therefore, the correct response is:

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