The sum of the angle measures of any triangle is 180 degrees. Suppose that one angle in a triangle has a degree measure of 4x-7 and another has a degree measure of 6x-4. Write an expression for the degree measure of the third angle in the triangle.

Write the sum of the three angles and set this sum equal to 180. Use (degree measure) to denote the third, unknown, angle:

4x - 7 + 6x-4 + (degree measure) = 180

Now subtract 4x - 7 + 6x-4 from both sides. We get:

(degree measure) = 180 - (4x - 7 + 6x-4). Simplify this:

= 180 + 7 - 4x - 6x + 4, or

= 180 + 11 - 10x, or

(degree measure) = 191 - 10x (answer)

This represents the degree measure of the third angle in the triangle.