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# Triangles: Isosceles

In the figure below, what is the value of $$x$$? ![](data:image/svg+xml;base64,PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0idXRmLTgiPz4NCjwhLS0gR2VuZXJhdG9yOiBBZG9iZSBJbGx1c3RyYXRvciAyNC4wLjEsIFNWRyBFeHBvcnQgUGx1Zy1JbiAuIFNWRyBWZXJzaW9uOiA2LjAwIEJ1aWxkIDApICAtLT4NCjxzdmcgdmVyc2lvbj0iMS4xIiBpZD0i0KHQu9C+0LlfMSIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIiB4bWxuczp4bGluaz0iaHR0cDovL3d3dy53My5vcmcvMTk5OS94bGluayIgeD0iMHB4IiB5PSIwcHgiDQoJIHdpZHRoPSIxNjEuMDNweCIgaGVpZ2h0PSIyNjAuODhweCIgdmlld0JveD0iMCAwIDE2MS4wMyAyNjAuODgiIHN0eWxlPSJlbmFibGUtYmFja2dyb3VuZDpuZXcgMCAwIDE2MS4wMyAyNjAuODg7Ig0KCSB4bWw6c3BhY2U9InByZXNlcnZlIj4NCjxzdHlsZSB0eXBlPSJ0ZXh0L2NzcyI+DQoJLnN0MHtmaWxsOm5vbmU7c3Ryb2tlOiMwMDAwMDA7c3Ryb2tlLXdpZHRoOjI7c3Ryb2tlLW1pdGVybGltaXQ6MTA7fQ0KCS5zdDF7ZmlsbDojMDIwMjAzO30NCgkuc3Qye2ZpbGw6bm9uZTtzdHJva2U6IzAwMDAwMDtzdHJva2UtbWl0ZXJsaW1pdDoxMDt9DQo8L3N0eWxlPg0KPHBhdGggY2xhc3M9InN0MCIgZD0iTTY0LjAyLDI0OS4zOGMtMjYuNTgsMC00OS4xOCwwLTQ5LjE4LDBsMTM0LjItMjMyLjU3djIzMi41N0MxNDkuMDQsMjQ5LjM4LDEwMi4zOCwyNDkuMzgsNjQuMDIsMjQ5LjM4eiIvPg0KPGxpbmUgY2xhc3M9InN0MCIgeDE9IjgxLjciIHkxPSIxMzMuNjkiIHgyPSIxNDkuMDQiIHkyPSIyNDkuMzgiLz4NCjxnPg0KCTxwYXRoIGNsYXNzPSJzdDEiIGQ9Ik0wLDI1OC4wM2wwLjItMC44aDAuM2MwLjMsMCwwLjUtMC4xLDAuNi0wLjJjMC4yLTAuMiwwLjQtMC41LDAuNi0xbDQuOS05LjRoMmwwLjksOS4zYzAsMC40LDAuMSwwLjcsMC4yLDAuOQ0KCQljMC4xLDAuMiwwLjMsMC40LDAuNiwwLjRoMC4zbC0wLjIsMC44SDUuOGwwLjItMC44aDAuM2MwLjMsMCwwLjYtMC4xLDAuNy0wLjJjMC4yLTAuMSwwLjMtMC4zLDAuMy0wLjZjMC0wLjEsMC0wLjEsMC0wLjINCgkJczAtMC4xLDAtMC4ybC0wLjEtMS43SDMuOGwtMC43LDEuNGMtMC4xLDAuMi0wLjIsMC40LTAuMiwwLjVzLTAuMSwwLjMtMC4xLDAuNGMwLDAuNCwwLjMsMC42LDAuOCwwLjZoMC4zbC0wLjIsMC44SDB6IE01LjcsMjUwLjQzDQoJCWwtMS40LDIuOWgyLjhsLTAuMi0yLjdjMC0wLjUsMC0wLjktMC4xLTEuM2MwLTAuNCwwLTAuOCwwLTEuMWMtMC4xLDAuNC0wLjMsMC43LTAuNCwxUzYsMjQ5LjkzLDUuNywyNTAuNDN6Ii8+DQo8L2c+DQo8Zz4NCgk8cGF0aCBjbGFzcz0ic3QxIiBkPSJNMTUxLjAzLDI2MC44OGwwLjItMC44aDAuMmMwLjMsMCwwLjYtMC4xLDAuOC0wLjJzMC40LTAuNCwwLjUtMC44bDEuNi03LjZjMC0wLjIsMC4xLTAuMywwLjEtMC40DQoJCWMwLTAuMSwwLTAuMiwwLTAuM2MwLTAuMi0wLjEtMC40LTAuMy0wLjVzLTAuNC0wLjEtMC43LTAuMWgtMC4ybDAuMi0wLjhoNC40YzEsMCwxLjgsMC4yLDIuNCwwLjZjMC41LDAuNCwwLjgsMSwwLjgsMS43DQoJCWMwLDAuOS0wLjIsMS42LTAuNywyLjFzLTEsMC44LTEuNywxdjAuMWMwLjUsMC4xLDAuOSwwLjMsMS4yLDAuN3MwLjUsMC45LDAuNSwxLjVjMCwxLjMtMC40LDIuMi0xLjIsMi44cy0xLjksMC45LTMuNCwwLjloLTQuNw0KCQlWMjYwLjg4eiBNMTU0LjgzLDI1OS44OGgwLjljMC44LDAsMS40LTAuMywxLjctMC44czAuNS0xLjIsMC41LTIuMmMwLTEuMS0wLjQtMS42LTEuMy0xLjZoLTAuOEwxNTQuODMsMjU5Ljg4eiBNMTU2LjAzLDI1NC4zOGgwLjcNCgkJYzAuNywwLDEuMS0wLjIsMS40LTAuN2MwLjMtMC41LDAuNC0xLjEsMC40LTEuOWMwLTEtMC40LTEuNS0xLjItMS41aC0wLjZMMTU2LjAzLDI1NC4zOHoiLz4NCjwvZz4NCjxnPg0KCTxwYXRoIGNsYXNzPSJzdDEiIGQ9Ik0xNTUuNjgsMTEuN2MtMS4zLDAtMi4zLTAuNC0zLjEtMS4xYy0wLjctMC43LTEuMS0xLjctMS4xLTNjMC0xLDAuMi0xLjksMC41LTIuOHMwLjctMS43LDEuMy0yLjUNCgkJYzAuNi0wLjcsMS4yLTEuMywyLTEuN3MxLjctMC42LDIuNi0wLjZjMC45LDAsMS42LDAuMiwyLDAuNXMwLjcsMC44LDAuNywxLjNzLTAuMiwwLjktMC42LDEuMWMtMC40LDAuMy0wLjksMC40LTEuNSwwLjQNCgkJYzAtMC4yLDAtMC41LDAtMC43YzAtMC4yLTAuMS0wLjUtMC4xLTAuOGMtMC4xLTAuMi0wLjItMC40LTAuMy0wLjZzLTAuMy0wLjMtMC42LTAuM2MtMC40LDAtMC44LDAuMS0xLjIsMC40cy0wLjcsMC43LTEsMS4yDQoJCXMtMC41LDEtMC43LDEuNnMtMC40LDEuMi0wLjUsMS44cy0wLjIsMS4yLTAuMiwxLjdjMCwwLjksMC4yLDEuNiwwLjYsMi4xYzAuNCwwLjUsMSwwLjcsMS43LDAuN2MwLjYsMCwxLjItMC4yLDEuNi0wLjUNCgkJYzAuNC0wLjMsMC43LTAuNiwxLTFjMCwwLDAuMSwwLjEsMC4xLDAuMmMwLjEsMC4xLDAuMSwwLjIsMC4xLDAuM2MwLDAuNC0wLjEsMC43LTAuNCwxYy0wLjMsMC4zLTAuNiwwLjYtMS4xLDAuOA0KCQlDMTU2Ljk4LDExLjYsMTU2LjM4LDExLjcsMTU1LjY4LDExLjd6Ii8+DQo8L2c+DQo8Zz4NCgk8cGF0aCBjbGFzcz0ic3QxIiBkPSJNNjguMDQsMTMzLjA5bDAuMi0wLjhoMC4yYzAuMywwLDAuNi0wLjEsMC44LTAuMmMwLjItMC4xLDAuNC0wLjQsMC41LTAuOGwxLjYtNy43YzAtMC4xLDAuMS0wLjIsMC4xLTAuMw0KCQlzMC0wLjIsMC0wLjJjMC0wLjItMC4xLTAuNC0wLjMtMC41Yy0wLjItMC4xLTAuNC0wLjEtMC43LTAuMWgtMC4ybDAuMi0wLjhoNC41YzEuMywwLDIuMywwLjQsMywxLjFzMS4xLDEuNywxLjEsMy4xDQoJCWMwLDEtMC4xLDEuOS0wLjQsMi44Yy0wLjMsMC45LTAuNywxLjctMS4yLDIuM2MtMC41LDAuNy0xLjIsMS4yLTEuOSwxLjZjLTAuOCwwLjQtMS42LDAuNi0yLjYsMC42aC00LjlWMTMzLjA5eiBNNzEuODQsMTMyLjA5aDAuNQ0KCQljMC45LDAsMS43LTAuMywyLjMtMC44YzAuNi0wLjYsMS4xLTEuMywxLjUtMi4zYzAuNC0xLDAuNS0yLjEsMC41LTMuM2MwLTEuMS0wLjItMS44LTAuNi0yLjNjLTAuNC0wLjUtMS0wLjctMS43LTAuN2gtMC41DQoJCUw3MS44NCwxMzIuMDl6Ii8+DQo8L2c+DQo8cGF0aCBjbGFzcz0ic3QyIiBkPSJNMTQ5LjA0LDUxLjQ0Yy02LjI1LDAtMTIuMTUtMS42OC0xNy4zMi00LjU3Ii8+DQo8bGluZSBjbGFzcz0ic3QyIiB4MT0iMTEyLjM2IiB5MT0iNzIuODUiIHgyPSIxMTguNSIgeTI9Ijc3LjMiLz4NCjxsaW5lIGNsYXNzPSJzdDIiIHgxPSI0NC45IiB5MT0iMTg5LjI1IiB4Mj0iNTEuMDMiIHkyPSIxOTMuNyIvPg0KPGxpbmUgY2xhc3M9InN0MiIgeDE9IjExMS44OCIgeTE9IjE5Mi45OCIgeDI9IjExOC4yNiIgeTI9IjE4OC44OSIvPg0KPGc+DQoJPHBhdGggY2xhc3M9InN0MSIgZD0iTTEyNy43NCw2OC4zOWwwLjItMC44aDAuMmMwLjIsMCwwLjMsMCwwLjUtMC4xYzAuMSwwLDAuMy0wLjEsMC40LTAuM2MwLjItMC4xLDAuNC0wLjQsMC42LTAuN2wxLjgtMi4zDQoJCWwtMC45LTIuNmMtMC4xLTAuNC0wLjMtMC43LTAuNC0wLjhjLTAuMS0wLjEtMC4zLTAuMi0wLjYtMC4yaC0wLjJsMC4yLTAuOGgyLjdsMC45LDMuMWwyLTMuMWgxLjdsLTAuMiwwLjhoLTAuMw0KCQljLTAuMiwwLTAuMywwLTAuNSwwLjFjLTAuMSwwLjEtMC4zLDAuMi0wLjQsMC4zYy0wLjEsMC4xLTAuMywwLjQtMC42LDAuN2wtMS41LDJsMC45LDIuN2MwLjEsMC41LDAuMywwLjgsMC40LDAuOQ0KCQljMC4xLDAuMSwwLjQsMC4yLDAuNiwwLjJoMC4ybC0wLjIsMC44aC0yLjhsLTAuOS0zLjNsLTIuMywzLjNoLTEuNVY2OC4zOXoiLz4NCgk8cGF0aCBjbGFzcz0ic3QxIiBkPSJNMTQwLjc0LDYxLjU5Yy0wLjcsMC0xLjItMC4yLTEuNi0wLjdjLTAuNC0wLjUtMC42LTEtMC42LTEuOGMwLTAuNywwLjItMS4zLDAuNi0xLjhjMC40LTAuNSwwLjktMC43LDEuNi0wLjcNCgkJczEuMiwwLjIsMS42LDAuN2MwLjQsMC41LDAuNiwxLDAuNiwxLjhjMCwwLjctMC4yLDEuMy0wLjYsMS44QzE0MS45NCw2MS4yOSwxNDEuMzQsNjEuNTksMTQwLjc0LDYxLjU5eiBNMTQwLjc0LDYwLjY5DQoJCWMwLjQsMCwwLjctMC4yLDAuOS0wLjVjMC4yLTAuMywwLjMtMC43LDAuMy0xLjJzLTAuMS0wLjgtMC4zLTEuMWMtMC4yLTAuMy0wLjUtMC40LTAuOS0wLjRjLTAuNCwwLTAuNywwLjEtMC45LDAuNA0KCQljLTAuMiwwLjMtMC4zLDAuNy0wLjMsMS4xczAuMSwwLjksMC4zLDEuMkMxNDAuMDQsNjAuNTksMTQwLjM0LDYwLjY5LDE0MC43NCw2MC42OXoiLz4NCjwvZz4NCjxsaW5lIGNsYXNzPSJzdDIiIHgxPSI4MS42NiIgeTE9IjI1My4xMSIgeDI9IjgxLjg0IiB5Mj0iMjQ1LjU0Ii8+DQo8L3N2Zz4NCg==)
Correct. [[snippet]] Given that all three sides of triangle $$ABD$$ are equal, all three angles are also equal (i.e., all the angles equal 60° since $$\frac{180^\circ}{3}=60^\circ$$). Also, $$BDC$$ is the supplementary angle of $$BDA$$, so >$$BDC = 180^\circ - 60^\circ = 120^\circ$$. Since $$BDC$$ is an isosceles triangle and side $$DB = DC$$, >$$x = DBC = \frac{180^\circ - 120^\circ}{ 2} = \frac{60^\circ}{2} = 30^\circ$$.
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
30°
45°
60°
90°
120°