{"status": "success", "data": {"description_md": "In $\\triangle PAT,$ $\\angle P=36^{\\circ},$ $\\angle A=56^{\\circ},$ and $PA=10.$ Points $U$ and $G$ lie on sides $\\overline{TP}$ and $\\overline{TA},$ respectively, so that $PU=AG=1.$ Let $M$ and $N$ be the midpoints of segments $\\overline{PA}$ and $\\overline{UG},$ respectively. What is the degree measure of the acute angle formed by lines $MN$ and $PA?$\n\n$\\textbf{(A) } 76 \\qquad <br>\\textbf{(B) } 77 \\qquad <br>\\textbf{(C) } 78 \\qquad <br>\\textbf{(D) } 79 \\qquad <br>\\textbf{(E) } 80$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>In  <span class=\"katex--inline\">\\triangle PAT,</span>   <span class=\"katex--inline\">\\angle P=36^{\\circ},</span>   <span class=\"katex--inline\">\\angle A=56^{\\circ},</span>  and  <span class=\"katex--inline\">PA=10.</span>  Points  <span class=\"katex--inline\">U</span>  and  <span class=\"katex--inline\">G</span>  lie on sides  <span class=\"katex--inline\">\\overline{TP}</span>  and  <span class=\"katex--inline\">\\overline{TA},</span>  respectively, so that  <span class=\"katex--inline\">PU=AG=1.</span>  Let  <span class=\"katex--inline\">M</span>  and  <span class=\"katex--inline\">N</span>  be the midpoints of segments  <span class=\"katex--inline\">\\overline{PA}</span>  and  <span class=\"katex--inline\">\\overline{UG},</span>  respectively. What is the degree measure of the acute angle formed by lines  <span class=\"katex--inline\">MN</span>  and  <span class=\"katex--inline\">PA?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 76 \\qquad \\textbf{(B) } 77 \\qquad \\textbf{(C) } 78 \\qquad \\textbf{(D) } 79 \\qquad \\textbf{(E) } 80</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2018 AMC 12A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12A_p24", "prev": "/problem/18_amc12A_p22"}}