1103055011
Level:
B
The picture shows the regular octagon \( ABCDEFGH \) and the equilateral triangle \( ABJ \). Give the measure of the angle \( JBC \).
\( 75^{\circ} \)
\( 30^{\circ} \)
\( 45^{\circ} \)
\( 60^{\circ} \)
Polygons
1103055012
Level:
B
The regular pentagon \( ABCDE \) is inscribed in a circle with the center \( S \) (see the picture). Give the measure of the angle \( ASB \).
\( 72^{\circ} \)
\( 36^{\circ} \)
\( 54^{\circ} \)
\( 108^{\circ} \)
1103055013
Level:
B
The regular pentagon \( ABCDE \) is inscribed in a circle with the center \( S \) (see the picture). Express the measure of the angle \( SAB \).
\( 54^{\circ} \)
\( 72^{\circ} \)
\( 36^{\circ} \)
\( 108^{\circ} \)
2000005507
Level:
B
We cut two triangles from the rectangular plate so that the resulting trapezoid has an area of \(30\,\mathrm{cm}^2\). One of its bases is twice as long as the other. What is the area of the two triangles that are cut off?
\(10\,\mathrm{cm}^2\)
\(20\,\mathrm{cm}^2\)
\(5\,\mathrm{cm}^2\)
\(8\,\mathrm{cm}^2\)
2000005908
Level:
B
Which of the following formulas gives the area of a regular nonagon inscribed in a circle with radius \(r\)? (See the picture.)
\(\frac{9r^2\sin{40^{\circ}}}{2}\)
\({9r^2\sin{40^{\circ}}}\)
\(\frac{9r^2\cos{40^{\circ}}}{2}\)
\(\frac{9r^2\sin{20^{\circ}}}{2}\)
2000006005
Level:
B
In the isosceles trapezoid \(ABCD\) is \(|AB|=|AC|\). The angle \(\alpha\) has the magnitude \(32^{\circ}\). What is the magnitude of the angle \(\delta\)?
\(106^{\circ}\)
\(120^{\circ}\)
\(148^{\circ}\)
\(74^{\circ}\)
2000006006
Level:
B
The bases of the trapezoid \(KLMN\) are \(12\,\mathrm{cm}\) and \(4\,\mathrm{cm}\) long. The area of the triangle \(KMN\) is \(9\,\mathrm{cm}^2\). What is the area of the trapezoid \(KLMN\)?
\(36\,\mathrm{cm}^2\)
\(72\,\mathrm{cm}^2\)
\(18\,\mathrm{cm}^2\)
\(40\,\mathrm{cm}^2\)
2010012809
Level:
B
Which of the following formulas expresses the area of a regular pentagon inscribed in a circle of radius \( r \)? (See the picture.)
\( \frac{5r^2\sin72^{\circ}}2\)
\( \frac{10r^2\sin72^{\circ}}2\)
\( \frac{5r^2\sin36^{\circ}}2\)
\( \frac{5r \sin36^{\circ}}2\)
2010015004
Level:
B
The isosceles trapezium \( ABCD \) is in the picture. The measure of the angle \( DAB \) is \( 60^{\circ} \). Determine the measure of the angle \( BCD \).
\( 120^{\circ} \)
\( 60^{\circ} \)
\( 110^{\circ} \)
\( 150^{\circ} \)
2010015005
Level:
B
Given the isosceles trapezium \( ABCD \), where \( |AB| = 12\,\mathrm{cm} \), \( |BC| = 4\,\mathrm{cm} \), \( |CD| = 16\,\mathrm{cm} \), and \( |AD| = 4\,\mathrm{cm} \), determine the measure of \( \measuredangle BCD \).
\( 60^{\circ} \)
\( 70^{\circ} \)
\( 45^{\circ} \)
\( 120^{\circ} \)