9000121806
Level:
B
The measure of the interior angle in a regular polygon is \(160^{\circ}\). Find the number of vertices of this polygon. In the figure the interior angle (marked in red) of a regular hexagon is shown.
\(18\)
\(16\)
\(32\)
\(9\)
Polygons
9000121808
Level:
B
The number of diagonals in a polygon is three times bigger than the number of sides
of this polygon. Find the number of vertices of this polygon.
\(9\)
\(12\)
\(6\)
\(15\)
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.
\(150^{\circ }\)
\(75^{\circ }\)
\(120^{\circ }\)
\(132^{\circ }\)
1103021401
Level:
C
\( ABCD \) is a rhombus, the height \( v = 48\,\mathrm{cm} \) and the shorter diagonal \( u = 60\,\mathrm{cm} \). Determine the measure of the acute interior angle of the rhombus. Round the result to two decimal places.
\( 73.74^{\circ} \)
\( 36.87^{\circ} \)
\( 24.12^{\circ} \)
\( 27.13^{\circ} \)
1103021608
Level:
C
Consider a circle \( k \) with radius \( 2.5\,\mathrm{cm} \). In the circle is inscribed a convex quadrilateral \( ABCD \) so that the diagonal \( AC \) is the diameter of the circle, the length of \( BC \) is \( \sqrt{21}\,\mathrm{cm} \), and the length of \( DC \) is \( 4\,\mathrm{cm} \). What is the length of the shortest side of this quadrilateral? (See the picture.)
\( 2\,\mathrm{cm} \)
\( 3\,\mathrm{cm} \)
\( \sqrt5\,\mathrm{cm} \)
\( 2.5\,\mathrm{cm} \)
1103021613
Level:
C
A circle is inscribed in a rhombus \( ABCD \). The touching points of the circle and the rhombus divide each side into two parts that are \( 12\,\mathrm{dm} \) and \( 25\,\mathrm{dm} \) long. (See the picture.) Find the measure of the angle \( CAB \). Round the result to two decimal places.
\( 34.72^{\circ} \)
\( 43.85^{\circ} \)
\( 46.15^{\circ} \)
\( 23.14^{\circ} \)
1103054907
Level:
C
The picture shows a kite. Give the measures of all interior angles \( \alpha \), \( \beta \), \( \gamma \) and \( \delta \).
\( \alpha = 124^{\circ} \), \( \beta = 108^{\circ} \), \( \gamma = 20^{\circ} \), \( \delta = 108^{\circ} \)
\( \alpha = 124^{\circ} \), \( \beta = 108^{\circ} \), \( \gamma = 124^{\circ} \), \( \delta = 108^{\circ} \)
\( \alpha = 124^{\circ} \), \( \beta = 72^{\circ} \), \( \gamma = 20^{\circ} \), \( \delta = 72^{\circ} \)
\( \alpha = 124^{\circ} \), \( \beta = 108^{\circ} \), \( \gamma = 72^{\circ} \), \( \delta = 83^{\circ} \)
1103054909
Level:
C
In the convex quadrilateral \( ABCD \), \( |AB| = |DA| = 20\,\mathrm{cm} \), \( |BC| = |CD| = 15\,\mathrm{cm} \). The diagonal \( AC \) is \( 25\,\mathrm{cm} \) long. Give the measure of the angle \( ABC \).
\( 90^{\circ} \)
\( 37^{\circ} \)
\( 53^{\circ} \)
\( 72^{\circ} \)
1103054910
Level:
C
In the kite \( ABCD \), \( |AB| = |BC| = 12\,\mathrm{cm} \), \( |CD| = |DA| = 6\,\mathrm{cm} \), and the measure of \( \measuredangle DAB \) is \( 120^{\circ} \). Calculate the area of the kite.
\( 36\sqrt3\,\mathrm{cm}^2 \)
\( 24\sqrt3\,\mathrm{cm}^2 \)
\( 18\sqrt3\,\mathrm{cm}^2 \)
\( 36\,\mathrm{cm}^2 \)