Answer: (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)
