Circles

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 \( ACB \)?
\( 50^{\circ} \)
\( 40^{\circ} \)
\( 100^{\circ} \)
\( 20^{\circ} \)

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.)
\( 45^{\circ} \)
\( 60^{\circ} \)
\( 30^{\circ} \)
\( 90^{\circ} \)

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.)
\( 90^{\circ} \)
\( 100^{\circ} \)
\( 80^{\circ} \)
\( 70^{\circ} \)

1003076810

Level: 
B
Interior angles of a triangle \( ABC \) are in the ratio \( 2:3:4 \). A circle is inscribed into the triangle \( ABC \). Points of tangency divide the circle into three arcs. What is the ratio of the lengths of these arcs?
\( 5:6:7 \)
\( 4:5:6 \)
\( 2:3:4 \)
\( 3:4:5 \)

9000121807

Level: 
A
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, the blue angle is the interior angle of the polygon. Suppose we consider a regular polygon with the central angle of \(40^{\circ}\), then find the measure of the interior angle of this polygon.
\(140^{\circ }\)
\(80^{\circ }\)
\(200^{\circ }\)
\(120^{\circ }\)