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Answer :
To find the measure of ∠LJK in triangle AJKL, we apply the rule that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. After solving for x, we find that ∠LJK measures 25 degrees.
The problem here involves understanding the concept of exterior angles in a triangle. In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles. In triangle AJKL, the exterior angle is ∠KLM = (50 - 11)° = 39°. And the two non-adjacent interior angles are ∠LJK = (x + 9)° and ∠JKL = (x - 2)°. So, according to the exterior angle theorem, we set up an equation for x: (x + 9) + (x - 2) = 39. Solving this equation gives x = 16. Therefore, the measure of ∠LJK = (16 + 9) = 25°.
Learn more about Exterior Angle Theorem here:
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