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)

Question

Responses

The third angle measure is 112°, 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 128°, and the triangle is an obtuse triangle.

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

Answer 1

In a triangle, the sum of the angles is always 180°. Given angles of 22° and 46°, we can find the third angle by subtracting the sum of these two angles from 180°.

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

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

Now that we know the third angle is 112°, we can classify the triangle. A triangle is classified as:

• Acute if all angles are less than 90°.
• Right if one angle is exactly 90°.
• Obtuse if one angle is greater than 90°.

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

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

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