A sector of a circle has a perimeter 72 cm and an angle of 75°. Find the radius of the circle correc

Step 1: Write sector perimeter formula
Perimeter = 2r + arc length
Arc length = (θ/360°) × 2πr
Therefore: Perimeter = 2r + (θ/360°) × 2πr

Step 2: Substitute known values
72 = 2r + (75/360) × 2 × (22/7) × r
72 = 2r + (75/360) × (44/7)r

Step 3: Simplify the fraction
75/360 = 5/24
72 = 2r + (5/24) × (44/7)r
72 = 2r + (220/168)r
72 = 2r + (55/42)r

Step 4: Combine terms
Convert 2r to same denominator: 2r = 84r/42
72 = (84r/42) + (55r/42)
72 = 139r/42

Step 5: Solve for r
r = (72 × 42)/139
r = 3024/139
r ≈ 21.76
r ≈ 21.8 cm (to 3 sig figs)