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Answers
angle ABC + angle ADC = 180
y + 10 + 5x + 5 = 180
5x + y + 15 = 180
5x + y = 165 -----------------(i)
angle BCD + angle ADC = 180
4x - 4 + 2y + 4 = 180
4x + 2y = 180 --------------------(ii)
Subtracting eq. (ii) from 2× e(i)
2(5x + y) - 4x + 2y = 330 - 180
10x + 2y - 4x + 2y = 150
6x = 150
x = 25
Substituting value of x in eq.(i) we get
5 × 25 + y = 165
125 + y = 165
y = 40
Therefore x= 25 and y = 40
Answer:
x = 25°
y = 40°
Step-by-step explanation:
ATQ
∠ABC + ∠ADC = 180° [∵opposite angles of a cyclic quadriletral are
supplementary]
(y+10°) + ((5x+5°) = 180°
5x+y+10°+5° = 180°
5x+y+15° = 180°
5x+y = 180°-15°
5x+y = 165° -----------(i)
∠BAD + ∠BCD = 180° [∵opposite angles of a cyclic quadriletral are
supplementary].
(2y+4°) + (4x-4°) = 180°
2y+4x+4°-4° = 180°
2y+4x = 180° ------------(ii)
form (i)
5x+y = 165°
y = 165°-5x -------------(iii)
By substituting the value of 'y' in (ii)
2(165°-5x)+4x = 180°
330°-10x+4x = 180°
4x-10x = 180°-330°
-6x = -150°
6x = 150°
x = 150°÷6
x = 25°
By keeping value of 'x' in (iii)
y = 165°-5(25°)
y = 165°-125°
y = 40°