9000121710
Level:
B
Consider a regular hexagon \(ABCDEF\)
with the center \(S\). Let the
point \(G\) be the middle
of the side \(DE\). Find the
measure of the angle \( BSG\).
\(150^{\circ }\)
\(160^{\circ }\)
\(135^{\circ }\)
\(120^{\circ }\)
Polygons
9000121803
Level:
B
Consider a regular polygon with the central angle of
\(24^{\circ }\). 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 diagonals in this polygon.
\(90\)
\(15\)
\(72\)
\(45\)
9000121809
Level:
B
The number of diagonals in a regular polygon is
\(2.5\)-times bigger than the number of the sides of this polygon. 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 central angle of the
polygon.
\(45^{\circ }\)
\(50^{\circ }\)
\(135^{\circ }\)
\(35^{\circ }\)
9000121810
Level:
B
The number of sides of the polygon is
\(4.5\)-times
smaller than the number of the diagonals in this polygon. Find the interior angle of
the polygon.
\(150^{\circ }\)
\(75^{\circ }\)
\(120^{\circ }\)
\(132^{\circ }\)
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 \( EFG\).
\(50^{\circ }\)
\(65^{\circ }\)
\(75^{\circ }\)
\(130^{\circ }\)
9000121706
Level:
A
Consider a rectangle \(ABCD\)
with a point \(E\) in the
middle of the side \(CD\). The
measure of the angle \( EAD\)
is \(30^{\circ }\). Find the measure
of the angle \( AEB\).
\(60^{\circ }\)
\(30^{\circ }\)
\(45^{\circ }\)
\(90^{\circ }\)
9000121707
Level:
A
Consider a rectangle \(ABCD\)
and a point \(S\)
which is the intersection of diagonals. The measure of the angle
\( BAS\) is
\(60^{\circ }\). Find the measure
of the angle \( BSC\).
\(120^{\circ }
\)
\(90^{\circ }
\)
\(60^{\circ }
\)
\(30^{\circ }
\)
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.
\(18\)
\(9\)
\(20\)
\(15\)
9000121804
Level:
B
Find the number of vertices of a regular polygon with
\(27\)
diagonals.
\(9\)
\(18\)
\(6\)
\(24\)