Circles

2010012801

Level: 
A
A triangle is inscribed in a circle. Its vertices divide the circle into three arcs whose lengths are in the ratio \( 3:4:5 \). Determine the measures of the interior angles of the triangle.
\( 45^{\circ};\ 60^{\circ};\ 75^{\circ} \)
\( 20^{\circ};\ 60^{\circ};\ 100^{\circ} \)
\( 20^{\circ};\ 40^{\circ};\ 120^{\circ} \)
\( 50^{\circ};\ 60^{\circ};\ 70^{\circ} \)

2000005910

Level: 
A
The regular heptagon is inscribed in a circle. Calculate the magnitudes of the interior angles of the chordal quadrilateral \(ACEG\). (See the picture.)
\( \alpha=4\cdot\frac{360^{\circ}}{14}\); \( \beta=3\cdot\frac{360^{\circ}}{14}\); \( \gamma=3\cdot\frac{360^{\circ}}{14}\); \( \delta=4\cdot\frac{360^{\circ}}{14}\)
\( \alpha=4\cdot\frac{360^{\circ}}{7}\); \( \beta=3\cdot\frac{360^{\circ}}{7}\); \( \gamma=3\cdot\frac{360^{\circ}}{7}\); \( \delta=4\cdot\frac{360^{\circ}}{7}\)
\( \alpha=4\cdot\frac{180^{\circ}}{14}\); \( \beta=3\cdot\frac{180^{\circ}}{14}\); \( \gamma=3\cdot\frac{180^{\circ}}{14}\); \( \delta=4\cdot\frac{180^{\circ}}{14}\)
\( \alpha=4\cdot\frac{360^{\circ}}{14}\); \( \beta=4\cdot\frac{360^{\circ}}{14}\); \( \gamma=3\cdot\frac{360^{\circ}}{14}\); \( \delta=3\cdot\frac{360^{\circ}}{14}\)

2000005909

Level: 
A
The regular octagon \(ABCDEFGH\) is inscribed in the circle. Calculate the magnitudes of the interior angles of the chordal quadrilateral \(HBCF\). (See the picture.)
\( \alpha=90^{\circ}\); \( \beta=112.5^{\circ}\); \( \gamma=90^{\circ}\); \( \delta=67.5^{\circ}\)
\( \alpha=90^{\circ}\); \( \beta=67.5^{\circ}\); \( \gamma=90^{\circ}\); \( \delta=67.5^{\circ}\)
\( \alpha=90^{\circ}\); \( \beta=122.5^{\circ}\); \( \gamma=80^{\circ}\); \( \delta=67.5^{\circ}\)
\( \alpha=90^{\circ}\); \( \beta=67.5^{\circ}\); \( \gamma=90^{\circ}\); \( \delta=112.5^{\circ}\)

2000005903

Level: 
A
What is the measure of the angle made by two line-segments marked in the clock face (see the picture)? One segment is connecting points \(7\) and \(1\), second segment is connecting points \(5\) and \(10\).
\(105^{\circ}\)
\(120^{\circ}\)
\(115^{\circ}\)
\(75^{\circ}\)

2000005902

Level: 
A
What is the measure of the angle made by two line-segments marked in the clock face (see the picture)? One segment is connecting points \(1\) and \(3\), second segment is connecting points \(5\) and \(3\).
\( 120^{\circ}\)
\( 135^{\circ}\)
\( 60^{\circ}\)
\( 240^{\circ}\)