Applying the central angle theorem, we have:
a. angle BAC.
b. arc BEC
c. arc BC
d. Measure of arc BEC = 260°
e. Measure of arc BC = 100°
What is the Central Angle Theorem?
According to the central angle theorem, the central angle that is suspended at the center of a circle by two line segments (usually radii) have a measure that is equal to the measure of the intercepted arc. That is:
Measure of central angle = measure of intercepted arc.
What is a Major and a Minor Arc?
A major arc have a measure that is greater than 180 degrees or half a circle, while minor arcs have a measure that is less than 180 degrees or half a circle.
a. A central angle in the image given is: angle BAC.
b. One major arc in the given circle is arc BEC (greater than half a half a circle/180 degrees).
c. One minor arc in the given circle is arc BC (less than half a half a circle/180 degrees).
d. m∠BEC = 360 - 100
m∠BEC = 260°
m∠BEC = measure of arc BEC [central angle theorem].
Measure of arc BEC = 260°
e. Measure of arc BC = m∠BAC [central angle theorem].
Measure of arc BC = 100°
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