Lesson 2

Inscribed Angles

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Problem 1

The measure of angle \(AOB\) is 56 degrees. What is the measure of angle \(ACB\)?

Circle center O. A, B and C lie on circle. Angle A O B labeled 56 degrees. Angles A C B and C B O shown.  

Solution

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Problem 2

Explain the difference between central and inscribed angles. 

Solution

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Problem 3

What is the measure of the arc from \(A\) to \(B\) that does not pass through \(C\)?

Triangle A B C inscribed in a circle with A C as the diameter and all points on the circle. Angle B A C is 40 degrees.
A:

160 degrees

B:

140 degrees

C:

100 degrees

D:

90 degrees

Solution

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Problem 4

Find the values of \(x, y,\) and \(z\).

Circle with center A. Diameter is drawn. Central angles x and y are formed along the diameter. Arc z is opposite central angle y. Arch opposite central angle x is 50 degrees.

Solution

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(From Unit 7, Lesson 1.)

Problem 5

Match the vocabulary term with the label.

A circle. A segment from edge to edge through the center, x. A dotted segment from the center to the edge, w. Angle formed by those two segments, m. A segment edge to edge not through the center, y.
A:

chord that is not a diameter

B:

diameter

C:

radius

D:

central angle

1:

m

2:

w

3:

x

4:

y

Solution

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(From Unit 7, Lesson 1.)

Problem 6

Triangle \(ABC\) has vertices at \((\text-4,0), (\text-2,12),\) and \((12,0)\). What is the point of intersection of its medians?

A:

\((4,0)\)

B:

\((5,6)\)

C:

\((2,4)\)

D:

\((4,2)\)

Solution

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(From Unit 6, Lesson 16.)

Problem 7

The rule \((x,y)\rightarrow (y,\text-x)\) takes a line to a perpendicular line. Select another rule that takes a line to a perpendicular line. 

A:

\((x,y)\rightarrow (\text-y,\text-x)\)

B:

\((x,y)\rightarrow (2y,2x)\)

C:

\((x,y)\rightarrow(\text-4y, 4x)\)

D:

\((x,y)\rightarrow(0.25y,\text-4)\)

Solution

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(From Unit 6, Lesson 11.)