# Lesson 12

### Problem 1

Match each diagram showing a sector with the measure of its central angle in radians.

### Problem 2

In the circle, sketch a central angle that measures $$\frac{2\pi}{3}$$ radians.

### Problem 3

Angle $$AOC$$ has a measure of $$\frac{5\pi}{6}$$ radians. The length of arc $$AB$$ is $$2\pi$$ units and the radius is 12 units. What is the area of sector $$BOC$$?

### Problem 4

Calculate the radian measure of a 30 degree angle. Use any method you like, including sketching in the circle diagram provided. Explain or show your reasoning.

### Solution

(From Unit 7, Lesson 11.)

### Problem 5

Lin thinks that the central angle in circle A is congruent to the central angle in circle B. Do you agree with Lin? Show or explain your reasoning.

### Solution

(From Unit 7, Lesson 11.)

### Problem 6

Select all true statements.

A:

The sector in circle B has a larger area than the sector in circle A.

B:

Not taking into account the sectors, circle A and circle B are similar.

C:

The fraction of the circumference taken up by the arc outlining circle A’s sector is smaller than the fraction of the circumference taken up by the arc in circle B.

D:

The ratio of the area of circle A’s sector to its total area is $$\frac16$$.

E:

The ratio of circle A’s area to circle B’s area is $$\frac 59$$.

### Solution

(From Unit 7, Lesson 10.)

### Problem 7

Match each arc length and radius with the measure of the central angle that defines the arc.

### Solution

(From Unit 7, Lesson 9.)

### Problem 8

Quadrilateral $$ABCD$$ is shown with the given angle measures. Select all true statements.

A:

Angle $$A$$ measures 140 degrees.

B:

The measures of angle $$A$$ and angle $$D$$ must add to 180 degrees.

C:

Angle $$A$$ measures 55 degrees.

D:

Angle $$D$$ measures 55 degrees.

E:

Angle $$D$$ measures 40 degrees.