Polygons

9000121709

Level: 
A
Consider a rectangle \(ABCD\) of a special ratio between the length and the width: if \(E\), \(F\), \(G\) and \(H\) denote the midpoints of the sides \(AB\), \(BC\), \(CD\) and \(DA\), respectively, then the measure of the angle \( AEH\) is \(25^{\circ }\). Find the measure of the angle \( EFG\).
\(50^{\circ }\)
\(65^{\circ }\)
\(75^{\circ }\)
\(130^{\circ }\)

9000121708

Level: 
A
Consider a square \(ABCD\) and a point \(E\) on the side \(BC\) such that the angle \( BAE\) has measure \(20^{\circ }\). The point \(F\) is on the side \(CD\) and the length of \(AF\) equals to the length of \(AE\) (i.e. the triangle \(AEF\) is isosceles with \(AF\) and \(AE\) of equal length). Find the measure of the angle \( AEF\).
\(65^{\circ }\)
\(45^{\circ }\)
\(50^{\circ }\)
\(70^{\circ }\)

9000121802

Level: 
B
Consider a regular polygon with the central angle of \(20^{\circ }\). In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the number of vertices of this polygon.
\(18\)
\(9\)
\(20\)
\(15\)

9000121807

Level: 
B
In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon, the blue angle is the interior angle of the polygon. Suppose we consider a regular polygon with the central angle of \(40^{\circ}\), then find the measure of the interior angle of this polygon.
\(140^{\circ }\)
\(80^{\circ }\)
\(200^{\circ }\)
\(120^{\circ }\)