Angles of Triangles Quick Check

Question

1 of 51 of 5 Items
Question
If a triangle has a 22°
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.

Answer 1

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

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

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

Now, to determine the type of triangle based on the angles:

• An acute triangle has all angles less than 90°.
• A right triangle has one angle equal to 90°.
• An obtuse triangle has one angle greater than 90°.

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

So the correct response is:

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