Question

In AJKL, where overline JL is extended through point L to point M, and m∠JKL = (3x - 16)°, m∠LJK = (2x + 15)°, and m∠KLM = (8x - 19)°, what is the measure of angle LJK?

A. 29°
B. 42°
C. 61°
D. 74°

Answer 1

To find the measure of angle LJK, we can use the fact that the sum of the angles in a triangle is 180 degrees. By solving the equation, we find that x ≈ 15.38. Substituting x back into the expression, we get that the measure of angle LJK is approximately 61°, corresponding to option C.

Step-by-step explanation:

To find the measure of angle LJK, we need to use the fact that the sum of the angles in a triangle is 180 degrees. So, we have:

1. m∠JKL + m∠LJK + m∠KLM = 180
2. (3x - 16) + (2x + 15) + (8x -19) = 180
3. 13x - 20 = 180
4. 13x = 200
5. x = 15.38

Now that we have the value of x, we can find the measure of angle LJK by substituting x back into the expression:

• m∠LJK = (2x + 15)
• m∠LJK = (2(15.38) + 15)
• m∠LJK = 45.76 + 15
• m∠LJK ≈ 61°

Therefore, the measure of angle LJK is approximately 61° which corresponds to option C.