Answer:
b. A central angle of 20 degrees
d. An inscribed angle of 10 degrees
Step-by-step explanation:
<u><em>The complete question is</em></u>
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
<u><em>Verify each case</em></u>
case a. A central angle of 10 degrees
we know that
<u><em>Central angle</em></u> 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
<u><em>Central angle</em></u> 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
<u><em>Central angle</em></u> 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 <u><em>inscribed angle</em></u> 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 <u><em>inscribed angle</em></u> 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 <u><em>inscribed angle</em></u> is half that of the arc it comprises
so
An inscribed angle of 40 degrees, intercept a 80 degree arc in a circle
