If a square's diagonal is extended by 6 units beyond a vertex, forming a triangle outside the square, what is the angle between this extension and the adjacent side of the square?
45 degrees
In any square, a diagonal bisects the right angle at each vertex it meets, so the diagonal makes an angle of \(\frac{90°}{2} = 45°\) with each side of the square.
When the diagonal is extended straight beyond a vertex, the extension lies along the same line as the diagonal.
A straight extension keeps the same inclination to the side as the diagonal itself, so the angle between the extension and the adjacent side is also 45°.
Hence, the required angle is 45 degrees.
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