In triangle ABC, find the degree measure of angle A. If C = 46 and B = 85.

It is known from the condition that in the triangle ABC the degree measure of the angles C = 46 ° and B = 85 °. And we need to find the degree measure of the angle A.

To do this, we will apply the triangle sum theorem, which says that the sum of the angles of a triangle is 180 °.

Let us denote by x ° the degree measure of the angle A and compose an equation with one variable:

angle A + angle B + angle C = 180 °;

x + 85 + 46 = 180;

We are looking for an unknown term:

x = 180 – 85 – 46;

x = 49 °.

Now we can write down the answer angle A is 49 °.

Answer: 49 °.