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प्रश्न
In a parallelogram `square`ABCD, If ∠A = (3x + 12)°, ∠B = (2x - 32)° then find the value of x and then find the measures of ∠C and ∠D.
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उत्तर
Given: ∠A = (3x + 12)˚ and ∠B = (2x - 32)˚
Opposite angles of a parallelogram are equal.
∴ ∠C = ∠A ...(i)
⇒ ∠C = (3x + 12)˚
∠D = ∠B …(ii)
∠D = (2x - 32)˚
In a quadrilateral, the sum of all the angles is equal to 360˚.
∴ In `square`ABCD,
∠A + ∠B + ∠C + ∠D = 360˚
∴ 3x + 12 + 2x - 32 + 3x + 12 + 2x - 32 = 360
∴ 10x - 40 = 360
∴ 10x = 360 + 40
∴ 10x = 400
∴ x = `400/10`
∴ x = 40
∴ ∠A = (3x + 12)˚
⇒ ∠A = 3 × 40 +12
⇒ ∠A = 120 + 12
⇒ ∠A = 132˚
∴ ∠C = 132˚ ...[From (i)]
∴ ∠B = (2x - 32)˚
⇒ ∠B = 2 × 40 - 32
⇒ ∠B = 80 - 32
⇒ ∠B = 48˚
∴ ∠D = 48˚ ...[From (ii)]
Hence, the measure of x is 40.
Also, measures of ∠C and ∠D are 132˚ and 48˚ respectively.
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