{"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":"c00aa723-1c78-5aa6-9e97-67f08ed3974d","task_key":"geometry--test--c00aa723-1c78-5aa6-9e97-67f08ed3974d","task_revision_id":"1","upstream_id":"","short_description":"Triangles $BDC$ and $ACD$ are coplanar and isosceles. If we have $m\\angle ABC =…","config":"geometry","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"Triangles $BDC$ and $ACD$ are coplanar and isosceles. If we have $m\\\\angle ABC = 70^\\\\circ$, what is $m\\\\angle BAC$, in degrees?\\n\\n[asy]\\nunitsize(2 cm);\\n\\ndefaultpen(linewidth(1pt)+fontsize(10pt));\\npair a,b,c,d;\\nb = (0,0);\\nc = (1,0);\\nd = c+dir(140);\\na = d+dir(70);\\ndraw(a--b--c--cycle);\\ndraw(d--c);\\npair s,t;\\ns = (.5,0)+(0,.05);\\nt = (.5,0)+(0,-.05);\\ndraw(s--t);\\ns = .5*(c+d) + .05*dir(50);\\nt = .5*(c+d) - .05*dir(50);\\ndraw(s--t);\\ns = .5*(a+d) + .05*dir(160);\\nt = .5*(a+d) - .05*dir(160);\\ndraw(s--t);\\nlabel(\\\"A\\\",a,N);\\nlabel(\\\"B\\\",b,SW);\\nlabel(\\\"C\\\",c,SE);\\nlabel(\\\"D\\\",d,NW);\\nlabel(\\\"$70^\\\\circ$\\\",b+(.05,.03),NE);\\n[/asy]\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}