Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 4.8 AIME Find the answer

[Intersecting lines, angle between them]

Let $A B C$ be an equilateral triangle, and $B C K M$ be a parallelogram. Find the angle between the lines $A B$ and $K M$ .

Your answer

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

Solution

Since $V S K M$ is a parallelogram, line $K M$ is parallel to line $B C$ . Therefore, the angle between lines $A B$ and $K M$ is equal to the angle between lines $A B$ and $B C$ , i.e., $60^{\circ}$ .

## Answer

$60^{\circ}$ .

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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.