Question

If a triangle has a 22°
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 obtuse triangle.
The third angle measure is  112 degrees , and the triangle is an obtuse triangle.

The third angle measure is 112°
112
°
, and the triangle is an acute 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 always 180°.

In this case, you have two angles: 22° and 46°.

1. First, add the two given angles:
\( 22° + 46° = 68° \)

2. Next, subtract this sum from 180° to find the third angle:
\( 180° - 68° = 112° \)

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

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

Therefore, the correct statement is:

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