Question

Which angles intercept a 20 degree arc in a circle? Select all that apply.

Answer 1

Answer:

b. A central angle of 20 degrees

d. An inscribed angle of 10 degrees

Step-by-step explanation:

The complete question is

Which angles intercept a 20 degree arc in a circle? Select all that apply.

a. A central angle of 10 degrees

b. A central angle of 20 degrees

c. A central angle of 40 degrees

d. An inscribed angle of 10 degrees

e. An inscribed angle of 20 degrees

f. An inscribed angle of 40 degrees

Verify each case

case a. A central angle of 10 degrees

we know that

Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it'

so

A central angle of 10 degrees, intercept a 10 degree arc in a circle (by central angle)

case b. A central angle of 20 degrees

we know that

Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it'

so

A central angle of 20 degrees, intercept a 20 degree arc in a circle (by central angle)

case c. A central angle of 40 degrees

we know that

Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it'

so

A central angle of 40 degrees, intercept a 40 degree arc in a circle (by central angle)

case d. An inscribed angle of 10 degrees

we know that

The inscribed angle is half that of the arc it comprises

so

An inscribed angle of 10 degrees, intercept a 20 degree arc in a circle

case e. An inscribed angle of 20 degrees

we know that

The inscribed angle is half that of the arc it comprises

so

An inscribed angle of 20 degrees, intercept a 40 degree arc in a circle

case f. An inscribed angle of 40 degrees

we know that

The inscribed angle is half that of the arc it comprises

so

An inscribed angle of 40 degrees, intercept a 80 degree arc in a circle