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.

Answer 1

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

Given:

• First angle = 22°
• Second angle = 46°

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

Now, let's analyze the type of triangle based on the angle measures:

• An obtuse triangle has one angle that is greater than 90°.
• An acute triangle has all angles less than 90°.

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

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