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Question
In a parallelogram ABCD, if ∠A = (3x − 20)°, ∠B = (y + 15)°, ∠C = (x + 40)°, then find the values of xand y.
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Solution
In parallelogram ABCD, ∠A and ∠C are opposite angles.
We know that in a parallelogram, the opposite angles are equal.
Therefore,
∠C = ∠A
We have ∠A = (3x - 20°) and ∠C = (x + 40°)
Therefore,
x + 40° = 3x - 20°
x - 3x = -40° - 20°
-2x = - 60°
x = 30°
Therefore,
∠A = (3x - 20°)
∠A = [3(30) - 20°]
∠A = 70°
Similarly,
∠C = 70°
Also, ∠B = ( y + 15)°
Therefore,
∠D = ∠B
∠D = (y + 15 )°
By angle sum property of a quadrilateral, we have:
∠A + ∠B + ∠C + ∠D = 360°
70° +(y + 15)° + 70° + (y + 15)° = 360°
140° + 2 (y + 15)° = 360°
2(Y + 15)° = 360° - 140°
2(y + 15)° = 220°
(y + 15)° = 110°
y = 95°
Hence the required values for x and y are 30° and 95° respectively.
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