Question

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

Answer 1

∠ LJK = 15°

Explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ KLM is an exterior angle of the triangle , then

∠ KLM = ∠ LJK + ∠ JKL , that is

5x - 11 = x + 9 + x - 2

5x - 11 = 2x + 7 ( subtract 2x from both sides )

3x - 11 = 7 ( add 11 to both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Then

∠ LJK = x + 9 = 6 + 9 = 15°