Question

In AJKL, JL is extended through point L to point M, m∠LJK = (x + 9)º, m∠JKL = (x - 2)°, and m∠KLM = (5x – 11)°. Find m∠KLM.

Answer 1

To find the measure of angle KLM, we can use the fact that the sum of the angles in a triangle is 180 degrees. By adding the given angles and solving for x, we find that m∠KLM is 129°.

Step-by-step explanation:

In order to find the measure of angle KLM, we can use the fact that the sum of the angles in a triangle is 180 degrees. Based on the given information, we have:

• m∠LJK = (x + 9)°
• m∠JKL = (x - 2)°
• m∠KLM = (5x - 11)°

Adding these angles together, we get:

(x + 9) + (x - 2) + (5x - 11) = 180

Combine like terms:

7x - 4 = 180

Now solve for x:

7x = 184

x = 26

Finally, substitute x back into the equation for m∠KLM:

m∠KLM = (5x - 11) = (5(26) - 11) = 129°