Circles

1003021501

Level:

Given a regular octadecagon

A_{1} A_{2} \dots A_{18}

, determine the measure of the angle

A_{2} A_{8} A_{3}

10^{\circ}

20^{\circ}

30^{\circ}

40^{\circ}

1003021508

Level:

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:

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:

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:

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:

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:

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

A C B

50^{\circ}

40^{\circ}

100^{\circ}

20^{\circ}

1103021507

Level:

Line segment

A B

is a diameter of the circle

k

. The lengths of the arcs

A D

and

D B

are in the ratio

7 : 3

. Find the measure of the angle

A C D

. (See the picture.)

63^{\circ}

27^{\circ}

126^{\circ}

24^{\circ}

1103021509

Level:

A regular dodecagon

A B C D E F G H I J K L

is inscribed in a circle. Find the measures of all interior angles of the quadrilateral

A B H J

. (See the picture.)

α = 120^{\circ}; β = 75^{\circ}; γ = 60^{\circ}; δ = 105^{\circ}

α = 105^{\circ}; β = 60^{\circ}; γ = 75^{\circ}; δ = 120^{\circ}

α = 120^{\circ}; β = 30^{\circ}; γ = 60^{\circ}; δ = 105^{\circ}

α = 105^{\circ}; β = 75^{\circ}; γ = 75^{\circ}; δ = 105^{\circ}

1103021510

Level:

A regular nonagon

A B C D E F G H I

is inscribed in a circle. Calculate the measures of all interior angles of the quadrilateral

A B E H

. (See the picture.)

α = 120^{\circ}; β = 100^{\circ}; γ = 60^{\circ}; δ = 80^{\circ}

α = 100^{\circ}; β = 120^{\circ}; γ = 60^{\circ}; δ = 80^{\circ}

α = 100^{\circ}; β = 100^{\circ}; γ = 80^{\circ}; δ = 60^{\circ}

α = 110^{\circ}; β = 130^{\circ}; γ = 70^{\circ}; δ = 50^{\circ}

1003021501

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