Question

5. Using ΔJKL, what is the measure of angle K?

Answer 1

x = 41

Explanation:

• The Triangle Sum Theorem says that the sum of the measures of the angles in a triangle always equals 180°.

Thus, we can find x by setting (x + 22)°, (2x - 6)°, and x° equal to 180:

(x + 22) + (2x - 6) + x = 180

(x + 2x + x) + (22 - 6) = 180

4x + 16 = 180

4x = 164

x = 41

Thus, x = 41

Check the validity of the answer:

We can check that x = 41 is the correct answer by pluggin in 41 for x in (x + 22)°, (2x - 6)° and x° and seeing whether the sum is 180:

(41 + 22) + (2(41) - 6) + 41 = 180

63 + (82 - 6) + 41 = 180

63 + 76 + 41 = 180

139 + 41 = 180

180 = 180

Thus, our answer is correct.