Unit 6 Practice Test: Arc Length and Sectors and Inscribed Angles
1) Quadrilateral ABCD is inscribed in this circle. What is the measure of ∠A? (∠C is 82°. ∠C is across from ∠A.)

2) Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C? (∠A is (2x+4)degrees, ∠B is (2x-1)degrees, ∠D is (3x-59)degrees.

3) What is the measure in degrees for the central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm?
Enter your answer as a decimal in the box, rounded to the nearest hundredth.

4) In a circle with a radius of 36 m, an arc is intercepted by a central angle of 288 degrees. What is the arc length? Use 3.14 for π and round your final answer to the nearest hundredth.

5) What is the area of a sector with a central angle of 150 degrees and a radius of 6 ft? Use 3.14 for π and round your final answer to the nearest tenth.

6) What is the area of a sector with a central angle of 52 degrees and a diameter of 40 mm? Use 3.14 for π and round your answer to the nearest hundredth.

(1) Angle A measures 98° (∠A = 98°)

(2)

(3) 51.59 degrees

(4) 180.86 m

(5) 47.1 square ft

(6) 181.42 square mm

Step-by-step explanation: (1) In the quadrilateral ABCD, angle C is opposite angle A and angle C measures 82 degrees, therefore angle A equals;

Angle A = 180 - angle C (Opposite angles in a cyclic quadrilateral sum up to 180)

Angle A = 180 - 82

Angle A = 98°

(3) If the radius of a circle is 8 cm and the length of the intercepted arc is 7.2 cm, the central angle can be calculated as follows;

Length of an arc = (∅/360) x 2πr

(Length of arc x 360)/2πr = ∅

(7.2 x 360)/2 x 3.14 x 8 = ∅

2592/50.24 = ∅

51.59

The central angle measures 51.59° (to the nearest hundredth)

(4) In a circle with radius 36 m and central angle of 288 degrees, the length of the arc is measured as,

Length of an arc = (∅/360) x 2πr

Length of arc = (288/360) x 2 x 3.14 x 36

Length of arc = 0.8 x 2 x 3.14 x 36

Length of arc = 180.864

The length of the arc is 180.86 m (to the nearest hundredth)

(5) Where the sector of a circle has a radius of 6 ft and a central angle of 150 degrees, the area of the sector is give as follows;

Area of a sector = (∅/360) x πr²

Area of sector = (150/360) x 3.14 x 6²

Area of sector = (5/12) x 3.14 x 36

Area of sector = 5 x 3.14 x 3

Area of sector = 47.1

Therefore the area of the sector is 47.1 square feet.

(6) If a circle has a central angle of 52 degrees and a diameter of 40 mm (radius equals 40/2 which is 20 mm) then the area of the sector would be derived as follows;

Area of a sector = (∅/360) x πr²

Area of a sector = (52/360) x 3.14 x 20²

Area of a sector = (13/90) x 3.14 x 400

Area of a sector = (13 x 3.14 x 40)/9

Area of a sector = 1632.8/9

Area of a sector = 181.422

Therefore the area of the sector is 181.42 square mm (to the nearest hundredth)