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Geometry Practice Quiz: Angles and Arcs

Solve circle geometry problems involving angles and arc measures. Calculate arc lengths, circle circumference, and area. Practice finding arc measures based on angles. Improve your geometry skills!

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Geometry Practice Quiz: Angles and Arcs

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  1. Extra Practice for Sem 2, Quiz 8

  2. Find the measure of angle 1. The vertex is the center of the circle, so the arc measure = the angle measure. m<1 = 60˚ B 60 A 2 1 3 C

  3. Find the measure of arc BC. AC is a diamenter, so arc AC = 180 ˚. Measure arc BC = 180 – 60 = 120˚ B 60 A 2 1 3 C

  4. Find the length of arc BC, if the radius is 6” 120 • 12π = 360 1 1 • 12π = 4π in 3 1 B 60 A 2 1 3 C

  5. Find the measure of arc DC if <2 = 15˚. The vertex of <2 is ON the circle, so the angle is ½ of the arc. Arc DC = 2(15) = 30˚ Now find the measure of arc AD. B 60 A 2 1 3 Measure of arc AD = 180 – 30 = 150˚ C D

  6. Find the measure of <2 BD is a diameter, so arc BD is 180 ˚ The vertex of <2 is ON the circle, so the angle is ½ the arc. m< 2 = 90 ˚ B 20 A 1 C 2 D 3

  7. If <1 = 35˚, find the measure of are DC The vertex of <1 is INSIDE the circle, so 35 = 20 + x 2 70 = 20 + x 50˚ = x B A 20 1 C 2 D 3

  8. Find the measure of <3. First, we need to find arc AD. BD is a diameter, so arc AD = 180 – 20 = 160 The vertex of <3 is OUTSIDE the circle, so x = 160 – 50 2 x = 55˚ B 20 A 1 C 50 2 D 3

  9. Find the circumference if BD = 20m C = πd = 20π m Now, find the area. B 20 A A = πr2 r = 10 = 100π m2 1 C 50 2 D 3

  10. Find the length of arc AB if BD = 20m 20 = 1 360 18 1 • 20π = 10π 18 1 9 B 20 A 1 C 50 2 D 3

  11. Find the value of x. Vertex is INSIDE the circle, so add arcs and divide by 2. x = 100 + 50 = 75 2 100 x 50

  12. Find the value of x. Vertex is OUTSIDE the circle, so subtract arcs and divide by 2. x = 100 – 28 = 36 2 100 28 x

  13. Find the value of x. Vertex is the center of the circle, so arc and angle have the same measure. x = 85 x 85

  14. Find the value of x. Vertex is OUTSIDE the circle, so subtract arcs and divide by 2. 113 – x = 20 2 113 – x = 40 -x = -73 x = 73 113 x 20

  15. Find the value of x. Vertex is INSIDE the circle, so add arcs and divide by 2. 35 = x + 50 2 70 = x + 50 20 = x x 35 50

  16. Find the area and circumference of a circle with a radius of 8 ft. A = 64 ft2 C = 16  ft

  17. Find the area and circumference of a circle with a diameter of 22 m. Radius = 11m A = 121 m2 C = 22 m

  18. Find the length of an arc with a measure of 45 in a circle with a radius of 4 mi. 45 = 1 360 8 C = 8 1 • 8 =  mi 8 1

  19. Find the length of an arc with a measure of 100 in a circle with a radius of 27cm. 100 = 5 360 18 C = 54 5 • 54 = 15 cm 18 1

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