Consider ΔDEF, where m∠D=4x−5, m∠E=3x+15, and m∠F=x+10. What is the value of x?

Answer 1

This an application of the triangle sum theorem, which says that the three angles in a triangle add to 180 degrees.

You are given three expressions which make up the three angles in a triangle, so what do we need to do with those three angles? The theorem says we need to add them all together. And what is it equal to? 180 degrees.

So the way we set it up:

(4x - 5) + (3x + 15) + (x + 10) = 180

Now it is a matter of combining terms and solving for x, a review of a simple algebra two-step equation.

Combine the x-terms together and the constants (the numbers) together.

(4x + 3x + x) + (-5 + 15 + 10) = 180

8x + 20 = 180

Now isolate the variable x by subtracting from both sides and dividing by 8. Let me know if you have any further questions of how to do this problem.