if a triangle has a 22 degree angle and a 46 degree angle, what can be established about the third angle measure and the type of triangle?

Question

a. The third angle measure is 112 degrees, and the triangle is an acute triangle
b. The third angle measure is 128 degrees, and the triangle is an obtuse triangle
c. The third angle measure is 68 degrees, and the triangle is an obtuse triangle
d. The third angle measure is 112 degrees, and the triangle is an obtuse triangle

Answer 1

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

Let x be the measure of the third angle. Therefore, we have the equation:

22 + 46 + x = 180 degrees

Simplifying the equation:

68 + x = 180 degrees

Subtracting 68 from both sides of the equation:

x = 112 degrees

Therefore, the third angle measure is 112 degrees.

To determine the type of triangle, we need to analyze the angle measures.

Since all three angles in the triangle are less than 90 degrees (22 degrees + 46 degrees + 112 degrees = 180 degrees), the triangle is an acute triangle.

So, the answer is:

a. The third angle measure is 112 degrees, and the triangle is an acute triangle.