Question

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.

Answer 1

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.