World's Hardest Easy Geometry Problem

Using only elementary geometry, determine angle x. Provide a step-by-step proof. You may only use elementary geometry, such as the fact that the angles of a triangle add up to 180 degrees and the basic congruent triangle rules (side-angle-side, etc.). You may not use more advanced trigonomery, such as the law of sines, the law of cosines, etc. There is a review of elementary geometry below. This is the hardest problem I have ever seen that is, in a sense, easy. It really can be done using only elementary geometry. This is not a trick question. Here is a very small hint. Here is a small hint.

Using only elementary geometry, determine angle x. Provide a step-by-step proof. This is a variation of the problem above. This is also a very hard problem that is, in a sense, easy. Here is a very small hint. Here is a small hint.

Here is everything you need to know to solve the above problems.

Lines and Angles: When two lines intersect, opposite angles are equal and the sum of adjacent angles is 180 degrees. When two parallel lines are intersected by a third line, the corresponding angles of the two intersections are equal.

Triangles: The sum of the interior angles of a triangle is 180 degrees. An isosceles triangle has two equal sides and the two angles opposite those sides are equal. An equilateral triangle has all sides equal and all angles equal. A right triangle has one angle equal to 90 degrees. Two triangles are called similar if they have the same angles (same shape). Two triangles are called congruent if they have the same angles and the same sides (same shape and size).

• Side-Angle-Side (SAS): Two triangles are congruent if a pair of corresponding sides and the included angle are equal.
• Side-Side-Side (SSS): Two triangles are congruent if their corresponding sides are equal.
• Angle-Side-Angle (ASA): Two triangles are congruent if a pair of corresponding angles and the included side are equal.
• Angle-Angle (AA): Two triangles are similar if a pair of corresponding angles are equal.

世界上最难的简单几何题

世界上最难的简单几何题（看原图）

仅使用初等几何原理来确定角X的度数。并写出证明过程。

你只能使用初等几何原理来解这道题，也就是说只能使用三角形的内角总和是180度；等腰和等边三角形的特性；平行线的对顶角相等；全等三角形的角边角、边角边、边边边定理以及三角形相似的角角角定理这一类的基础知识。不能使用正弦余弦定理。关于能使用的定理会在下文给出。

这是我所见过的最难的数学题，尽管看起来是如此的简单。并且真的可以只用初等几何解题。

这里有一个小提示，这里还有另一个。

这道题排行第二（看原图）

仅能使用初等几何原理得出角X的值。并写出详细步骤。

这道题是上一题的变形，但是要解出来也绝非易事。

这里有一个小提示，这是另一个。

基础几何原理

关于解题你所能用的原理。

相交线和交角：两条相交线，对角相等，两个邻角相加为180度。两条平行线与第三条线相交，相对的角相等。

三角形：三角形的内角总和是180度。等腰三角形有两条边相等，且有两个相等角。等边三角形三条边相等，三个角相等。直角三角形有一个九十度的角。两个三角形的形状相似，则它们的对应角相等。

• 边角边：有两边和它的夹角对应相等的两个三角形全等
• 边边边：三边对应相等的两个三角形全等
• 角边角：两个角和两角夹的边对应相等的三角形全等
• 角角：如果两个三角形的两个对应角相等，那么这两个三角形相似