Task 550
Task 550: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. In right triangle $JKL$, angle $J$ measures 60 degrees and angle $K$ measures 30 degrees. When drawn, the angle bisectors of angles $J$ and $K$ intersect at a point $M$. What is the measure of obtuse…
The task
In right triangle $JKL$, angle $J$ measures 60 degrees and angle $K$ measures 30 degrees. When drawn, the angle bisectors of angles $J$ and $K$ intersect at a point $M$. What is the measure of obtuse angle $JMK$? [asy] import geometry; import olympiad; unitsize(0.8inch); dotfactor = 3; defaultpen(linewidth(1pt)+fontsize(10pt)); pair J,K,L,M,U,V; J = (0,0); K = (1,2); L = (1,0); draw(J--K--L--cycle); draw(rightanglemark(J,L,K,5)); label("$J$",J,W); label("$K$",K,N); label("$L$",L,E); U = (1,2/3); V = (2/(2+sqrt(3)),0); draw(J--U); draw(K--V); M = intersectionpoint(J--U,K--V); dot("M",M,NW); [/asy]