Polygons

1003021307

Level: 
A
Choose the wrong claim:
The diagonals of a rhombus contain an acute angle.
In each parallelogram the opposite angles are congruent.
If one of the interior angles of a quadrilateral is greater than straight angle, the quadrilateral is not convex.
All interior angles in a square are right.

1003054908

Level: 
A
A quadrilateral is symmetric across one of its diagonals and can be inscribed in a circle. The measure of one of its interior angles is \( 80^{\circ} \). Determine the measure of its largest interior angle.
\( 100^{\circ} \)
\( 160^{\circ} \)
\( 200^{\circ} \)
\( 120^{\circ} \)

1103021303

Level: 
A
A rectangle with sides \( a \), \( b \) is given. The angle between diagonals \( \alpha = 60^{\circ} \). The longer side \( a = 6\,\mathrm{cm} \). Calculate the length of the shorter side \( b \).
\( \frac6{\sqrt3}\,\mathrm{cm} \)
\( \frac3{\sqrt3}\,\mathrm{cm} \)
\( \frac1{\sqrt3}\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)

1103021402

Level: 
A
The area of a rhombus is \( 200\,\mathrm{cm}^2 \). Give the measure of the acute interior angle of the rhombus if the length of its side is \( 15\,\mathrm{cm} \). Round the result to two decimal places.
\( 62.73^{\circ} \)
\( 27.28^{\circ} \)
\( 41.63^{\circ} \)
\( 12.13^{\circ} \)

1103021403

Level: 
A
Given the rhombus \( ABCD \) with the diagonal \( |DB|= 8\,\mathrm{cm} \). The measure of \( \measuredangle DAB \) is \( 60^{\circ} \). Calculate the circumference of the rhombus.
\( 32\,\mathrm{cm} \)
\( 18.48\,\mathrm{cm} \)
\(64\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)