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Cogito

Geometry · Chapter 6 · Lesson 1

Practice Worksheet

Angles, Arcs, and Sectors

Everything in a circle is a fraction of the whole.

10 problems · about 20 minutes · G-C.A.2, G-C.B.5

NameDate

Figure — use these to answer the problems

Arc length is a fraction of the circumference; sector area a fraction of the area.
d = 10
  • Diameter10 cm
  • Circumference31.42 cm
  • Area78.54 cm²
  • Circumference ÷ diameter3.14
Radius5
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Special Right Triangles”

    30-60-90 with hypotenuse 18. Shortest side?

    Answer

  2. From “Solving Right Triangles”

    Legs 7 and 24. Hypotenuse?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Central angle 140°. Inscribed angle on the same arc?

    Answer

  2. How does an inscribed angle compare with the central angle on the same arc?

    • It is half.
    • It is equal.

  3. Central angle 100°. Inscribed angle on the same arc?

    Answer

  4. A 90° sector is what fraction of the circle? Give the bottom number.

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Inscribed angle 35°. The central angle on the same arc?

    Answer

  2. A 120° sector is what fraction? Give the bottom number.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Inscribed Angle

    A central angle is 80°. What is the inscribed angle on the same arc?

    Answerdegrees

  2. The Semicircle

    An angle inscribed in a semicircle is how many degrees?

    Answerdegrees