1003021501
Level:
A
Given a regular octadecagon \( A_1A_2\dots A_{18} \), determine the measure of the angle \( A_2A_8A_3 \).
\( 10^{\circ} \)
\( 20^{\circ} \)
\( 30^{\circ} \)
\( 40^{\circ} \)
Circles
1003021508
Level:
A
A triangle is inscribed in a circle. Its vertices divide the circle into three arcs whose lengths are in the ratio \( 2:4:9 \). Determine the measures of the interior angles of the triangle.
\( 24^{\circ};\ 48^{\circ};\ 108^{\circ} \)
\( 30^{\circ};\ 40^{\circ};\ 110^{\circ} \)
\( 48^{\circ};\ 15^{\circ};\ 117^{\circ} \)
\( 15^{\circ};\ 60^{\circ};\ 105^{\circ} \)
1103021502
Level:
A
What is the measure of the angle contained by two line segments: the first joining numbers \( 8 \) and \( 11 \), and the second joining numbers \( 11 \) and \( 2 \), on a clock face? (See the picture.)
\( 90^{\circ} \)
\( 100^{\circ} \)
\( 80^{\circ} \)
\( 70^{\circ} \)
1103021503
Level:
A
Determine the measure of the angle contained by two line segments: the first joining numbers \( 7 \) and \( 1 \), and the second joining numbers \( 1 \) and \( 4 \), on a clock face. (See the picture.)
\( 45^{\circ} \)
\( 60^{\circ} \)
\( 30^{\circ} \)
\( 90^{\circ} \)
1103021504
Level:
A
Give the measure of the angle contained by two line segments with the endpoints at the numbers \( 7 \), \( 8 \) and \( 8 \), \( 10 \) on a clock face. (See the picture.)
\( 135^{\circ} \)
\( 90^{\circ} \)
\( 45^{\circ} \)
\( 120^{\circ} \)
1103021505
Level:
A
Give the measure of the angle between two line segments: the first connecting numbers \( 7 \) and \( 11 \), the second connecting numbers \( 3 \) and \( 10 \) on a clock face. (See the picture.)
\( 75^{\circ} \)
\( 60^{\circ} \)
\( 45^{\circ} \)
\( 80^{\circ} \)
1103021506
Level:
A
Points \( A \) and \( B \) divide the circle \( k \) into two arcs whose lengths are in the ratio \( 5:13 \). Point \( C \) is an interior point of the longer arc. What is the degree measure of the angle \( ACB \)?
\( 50^{\circ} \)
\( 40^{\circ} \)
\( 100^{\circ} \)
\( 20^{\circ} \)
1103021507
Level:
A
Line segment \( AB \) is a diameter of the circle \( k \). The lengths of the arcs \( AD \) and \( DB \) are in the ratio \( 7:3 \). Find the measure of the angle \( ACD \). (See the picture.)
\( 63^{\circ} \)
\( 27^{\circ} \)
\( 126^{\circ} \)
\( 24^{\circ} \)
1103021509
Level:
A
A regular dodecagon \( ABCDEFGHIJKL \) is inscribed in a circle. Find the measures of all interior angles of the quadrilateral \( ABHJ \). (See the picture.)
\( \alpha=120^{\circ};\ \beta=75^{\circ};\ \gamma=60^{\circ};\ \delta=105^{\circ} \)
\( \alpha=105^{\circ};\ \beta=60^{\circ};\ \gamma=75^{\circ};\ \delta=120^{\circ} \)
\( \alpha=120^{\circ};\ \beta=30^{\circ};\ \gamma=60^{\circ};\ \delta=105^{\circ} \)
\( \alpha=105^{\circ};\ \beta=75^{\circ};\ \gamma=75^{\circ};\ \delta=105^{\circ} \)
1103021510
Level:
A
A regular nonagon \( ABCDEFGHI \) is inscribed in a circle. Calculate the measures of all interior angles of the quadrilateral \( ABEH \). (See the picture.)
\( \alpha=120^{\circ};\ \beta=100^{\circ};\ \gamma=60^{\circ};\ \delta=80^{\circ} \)
\( \alpha=100^{\circ};\ \beta=120^{\circ};\ \gamma=60^{\circ};\ \delta=80^{\circ} \)
\( \alpha=100^{\circ};\ \beta=100^{\circ};\ \gamma=80^{\circ};\ \delta=60^{\circ} \)
\( \alpha=110^{\circ};\ \beta=130^{\circ};\ \gamma=70^{\circ};\ \delta=50^{\circ} \)