Lesson 2

Inscribed Angles

  • Let’s analyze angles made from chords.

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.

Problem 2

Explain the difference between central and inscribed angles. 

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.

160 degrees


140 degrees


100 degrees


90 degrees

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.
(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.
(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?









(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. 


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


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


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



(From Unit 6, Lesson 11.)