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Match each diagram showing a sector with the measure of its central angle in radians.
Circles A through F with sectors shown. A, about 60 degrees. B, about 90 degrees. C, about 120 degrees. D, about 180 degrees. E, about 270 degrees. F, about 360 degrees.
diagram A
diagram B
diagram C
diagram D
diagram E
diagram F
\(\frac{3\pi}{2}\)
\(\pi\)
\(\frac{\pi}{3}\)
\(\frac{\pi}{2}\)
\(2\pi\)
\(\frac{2\pi}{3}\)
In the circle, sketch a central angle that measures \(\frac{2\pi}{3}\) radians.
Angle \(AOC\) has a measure of \(\frac{5\pi}{6}\) radians. The length of arc \(AB\) is \(2\pi\) units, and the radius is 12 units. What is the area of sector \(BOC\)?
Calculate the radian measure of a 30-degree angle. Use any method you like, including sketching in the circle diagram provided. Explain or show your reasoning.
Lin thinks that the central angle in Circle A is congruent to the central angle in Circle B. Do you agree with Lin? Show or explain your reasoning.
Circle A
Circle B
Circle A
Circle B
Select all true statements.
The sector in Circle B has a larger area than the sector in Circle A.
Not taking into account the sectors, Circle A and Circle B are similar.
The fraction of the circumference taken up by the arc outlining the sector in Circle A is smaller than the fraction of the circumference taken up by the arc outlining the sector in Circle B.
The ratio of the area of Circle A’s sector to its total area is \(\frac16\).
The ratio of Circle A’s area to Circle B’s area is \(\frac 59\).
Quadrilateral \(ABCD\) is shown with the given angle measures. Select all true statements.
Angle \(A\) measures 140 degrees.
The measures of angle \(A\) and angle \(D\) must add to 180 degrees.
Angle \(A\) measures 55 degrees.
Angle \(D\) measures 55 degrees.
Angle \(D\) measures 40 degrees.