Find the measure

Question

<DFG and <JKL are complimentary angles. m<DFG = x + 6, and m<JKL = x - 10. Find the measure of each angle.

Answer 1

The answer to this question lies in the definition of complimentary angles. Knowing all the definitions in this chapter might help you be able to solve these types of problems for the quizzes and tests.

Complementary angles are two angles that add to 90 degrees. Therefore, x + 6 + x – 10 = 90.

Solve for x like you learned in Algebra 1: add like terms and then get the x by itself.

Once you know what x is, you are actually not done with the problem yet. What does the question ask for? "Find the measure of each angle." So we need to take the value of x and plug it back into the original equations to find the answer to the question: m∠DFG = x + 6 and m∠JKL = x – 10.

Let me know if you need extra help with solving to get the x by itself.

Answer 2

The definition of complimentary angles is two angles whose measures sum (add) to 90º.

∠DFG and ∠JKL are complimentary

m∠DFG + m∠JKL = 90º

(x + 6) + (x - 10) = 90

2x - 4 = 90

2x = 94

x = 47

We can now substitute (plug in) x to find the angle measures.

m∠DFG = x + 6

m∠DFG = (47) + 6

m∠DFG = 53º

m∠JKL = x - 10

m∠JKL = (47) - 10

m∠JKL = 37º

And we are done!

The final answer is:

m∠DFG = 53º and m∠JKL = 37º

Notice 53 + 37 = 90. This is exactly what we want. This is the definition of complimentary angles.