{"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":"cbd49169-70ba-5999-ac6c-832d4bffc18a","task_key":"geometry--test--cbd49169-70ba-5999-ac6c-832d4bffc18a","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, $AD=BD=CD$ and $\\angle BCA = 40^\\circ.$ What is the measure of…","config":"geometry","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"In the diagram, $AD=BD=CD$ and $\\\\angle BCA = 40^\\\\circ.$ What is the measure of $\\\\angle BAC?$\\n\\n[asy]\\ndraw((0,0)--(10,0)--(8.2635,9.8481)--cycle,black+linewidth(1));\\ndraw((10,0)--(20,0)--(8.2635,9.8481),black+linewidth(1));\\ndraw((5,-0.5)--(5,0.5),black+linewidth(1));\\ndraw((15,-0.5)--(15,0.5),black+linewidth(1));\\ndraw((8.6318,4.8359)--(9.6317,5.0122),black+linewidth(1));\\nlabel(\\\"$A$\\\",(8.2635,9.8481),N);\\nlabel(\\\"$B$\\\",(0,0),SW);\\nlabel(\\\"$C$\\\",(20,0),SE);\\nlabel(\\\"$D$\\\",(10,0),S);\\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":[]}