Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 4.5 AIME Find the answer

7. $A B C D$ is a square, point $E$ is on $A C$ , $A E=A D$ , a line through point $E$ is perpendicular to $A E$ and intersects $D C, B C$ at points $F, G$ respectively, then the degree of $\angle B E G$ is

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$7.22 .5^{\circ}$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.