Question 1
Find the value of y so that the shaded figure is a gnomon to the white triangle.
![](data:image/png;base64, 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)
◦ 39
◦ 24
◦ 26
◦ 36
◦ none of these
Question 2
If A is a golden rectangle, a gnomon to A is
◦ another golden rectangle whose longer side equals the shorter side of A.
◦ a square of sides equal to the shorter side of A.
◦ another golden rectangle whose shorter side equals the longer side of A.
◦ a square of sides equal to the longer side of A.
◦ none of these