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

2. The third angle measure is 112° , and the triangle is an acute triangle
3. The third angle measure is 128° , and the triangle is an obtuse triangle
4. The third angle measure is 68° , and the triangle is an obtuse triangle

Answer 1

Answers: 1. The third angle measure is 112°, and the triangle is an obtuse triangle. 2. No, because there needs to be a third angle. 3. acute triangle 4. 52° 5. 38°

Answer 2

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

22° + 46° + x = 180°
68° + x = 180°
x = 112°

So, the third angle measure is 112°.

Regarding the type of triangle, an obtuse triangle has one angle that is greater than 90°. Since the third angle measure is 112°, which is greater than 90°, the triangle is an obtuse triangle.

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