Angles of Triangles Quick Check

Question

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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 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 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 acute triangle.
The third angle measure is 112 degrees , and the triangle is an acute 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 third angle of a triangle when two angles are given, you use the fact that the sum of the angles in a triangle is always 180°.

In this case, the given angles are 22° and 46°.

First, calculate the sum of these two angles: 22° + 46° = 68°

Now subtract this sum from 180° to find the third angle: 180° - 68° = 112°

So, the third angle measures 112°.

Now, to determine the type of triangle:

• If one angle is greater than 90°, the triangle is obtuse.
• If all angles are less than 90°, it is acute.
• If one angle is exactly 90°, it is a right triangle.

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

Therefore, the correct response is:

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