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Answer :
Final answer:
The measure of angle J in triangle JKL, where line KM bisects JL and forms an equilateral triangle KLM, is 30 degrees.
Explanation:
The student has asked for the measure of angle J in a triangle with a specific geometric configuration. Point M lies on side JL of triangle JKL. A line from point K to M bisects JL and creates an equilateral triangle KLM.
Because KLM is an equilateral triangle, all its internal angles are 60 degrees. Triangle JKL has been bisected by KM, creating two right triangles.
In a right triangle, the sum of the non-right angles must be 90 degrees to add up to the 180 degrees a triangle has.
Since KLM is equilateral, the angles KML and KLM are both 60 degrees. Therefore, angle J, which is adjacent to angle KLM in the larger triangle JKL, must be 30 degrees (90 degrees - 60 degrees).
So, the measure of angle J in triangle JKL, given the conditions described, is 30 degrees.
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