{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"a1e742e9-a9bb-5a79-bf87-3e2e2dda1fc6","task_key":"prealgebra--test--a1e742e9-a9bb-5a79-bf87-3e2e2dda1fc6","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, $PW$ is parallel to $QX$, $S$ and $T$ lie on $QX$, and $U$ and…","config":"prealgebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"In the diagram, $PW$ is parallel to $QX$, $S$ and $T$ lie on $QX$, and $U$ and $V$ are the points of intersection of $PW$ with $SR$ and $TR$, respectively. If $\\\\angle SUV = 120^\\\\circ$ and $\\\\angle VTX = 112^\\\\circ$, what is the measure of $\\\\angle URV$? [asy]\\nsize(6cm); defaultpen(linewidth(0.75) + fontsize(11));\\n// Useful function\\npath extend(pair a, pair b, int n=10) { return a--(a + n * (b - a));}\\n\\n// Points\\nreal ust = 60; real vtx = 112;\\npair q = (0, 0); pair p = (0, 0.5); pair w = (2, p.y); pair x = (2, 0);\\npair s = (0.3, 0); pair t = s + (1, 0);\\npair u = shift(s) * (p.y / Tan(ust), p.y); pair v = shift(t) * (p.y / Tan(vtx), p.y);\\npair r = IP(extend(s, u), extend(t, v));\\n\\n// Draw lines\\ndraw(s--r--t);\\ndraw(p--w, Arrow(position=0.8, size=5));\\ndraw(q--x, Arrow(position=0.8, size=5));\\n\\n// Labels\\nlabel(\\\"$P$\\\", p, W); label(\\\"$Q$\\\", q, W); label(\\\"$W$\\\", w, E); label(\\\"$X$\\\", x, E);\\nlabel(\\\"$R$\\\", r, N); label(\\\"$U$\\\", u, NW); label(\\\"$V$\\\", v, NE); label(\\\"$S$\\\", s, NW);\\n\\nlabel(\\\"$T$\\\", t, NE);\\n\\n[/asy]\",\"type\":\"Prealgebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}