Exploring Central and Inscribed Angles

What is the measure of a central angle in an evenly spaced 8-point circle?

• 45 degrees

• 60 degrees

• 30 degrees

• 90 degrees

In an isosceles triangle formed by two radii in a circle, if the central angle is 90 degrees, what are the measures of the other two angles?

• 30 degrees each

• 45 degrees each

• 90 degrees each

• 60 degrees each

Tags

CCSS.HSG.C.A.2

What is the relationship between an inscribed angle and its corresponding central angle?

• The inscribed angle is twice the central angle.

• There is no specific relationship.

• The inscribed angle is half the central angle.

• The inscribed angle is equal to the central angle.

Tags

CCSS.HSG.C.A.2

If a central angle measures 60 degrees, what is the measure of the inscribed angle that intercepts the same arc?

• 90 degrees

• 30 degrees

• 60 degrees

• 120 degrees

Tags

CCSS.HSG.C.A.2

Given a central angle of 130 degrees, what is the measure of the adjacent angle formed outside the triangle?

• 25 degrees

• 130 degrees

• 65 degrees

• 50 degrees

If an inscribed angle measures 20 degrees, what is the measure of the intercepted arc?

• 40 degrees

• 10 degrees

• 20 degrees

• 80 degrees

Tags

CCSS.HSG.C.A.2

How can the measure of an angle formed by two chords intersecting inside a circle be found?

• By using the properties of isosceles triangles

• There is no way to find it

• By doubling the measure of the central angle

• By halving the measure of the central angle

Tags

CCSS.HSG.C.A.2

If the sum of a central angle and an adjacent angle is 190 degrees, what is the measure of the other adjacent angle?

• 190 degrees

• 170 degrees

• 90 degrees

• 20 degrees

Tags

CCSS.HSG.C.A.2

What is the measure of an angle formed by two intersecting chords if one of the intercepted arcs measures 50 degrees?

• 100 degrees

• 75 degrees

• 50 degrees

• 25 degrees

Tags

CCSS.HSG.C.A.2

In a circle, if a central angle measures X degrees, what algebraic expression represents the measure of an inscribed angle intercepting the same arc?

• X/2

• X-180

• 2X

• X

Tags

CCSS.HSG.C.A.2