How many degrees would a square need to be rotated to map onto itself?
2 answers:
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Answer:
Step-by-step explanation:
a + 143 = 180 {Linear pair}
a = 180 - 143
a = 37
37 + 93 + b = 180 {Angle sum property of triangle}
130 + b = 180
b = 180 - 130
b = 40
c + b = 90
c + 40 = 90
c = 90 - 40
c = 50
d + 120 = 180 {Linear pair}
d = 180 - 120
d = 60
? = 60 + 40 {Exterior angle property of triangle}
? = 100
➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.
➻ The required number of people who can speak both English and Spanish .
<u>Consider</u> ,
➻ A → Set of people who speak English.
➻ B → Set of people who speak Spanish
➻ A∩B → Set of people who can speak both English and Spanish
- ➻ n (A) = 27
- ➻ n (B) = 25
- ➻ n (A∪B) = 40
- ➻ n(A∩B) = ?
➻ n(A∪B) = n(A) + n (B) - n(A∩B)
➻ 40 = 27 + 25 - n (A∩B)
➻ 40 = 52 - n (A∩B)
➻ n (A∩B) = 52 - 40
➻ ∴ n (A∩B) = 12
∴ Required Number of persons who can speak both English and Spanish are <u>12 .</u>
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➻ n(A∪B) = n(A) + n (B) - n(A∩B)
➻ 40 = 27 + 25 - 12
➻ 40 = 52 - 12
➻ 40 = 40
➻ ∴ L.H.S = R.H.S
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