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Mathematics

In a trapezium ABCD, AB//DC and AD = BC. If ∠A = (5x + 8)° and ∠D = (4x + 10)°; the measure of angle B is

  1. 98°

  2. 82°

  3. 96°

  4. none of these

Quadrilaterals

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Answer

According to the properties of parallelogram, consecutive angles of a parallelogram are supplementary.

⇒ ∠ A + ∠ D = 180°

⇒ (5x + 8)° + (4x + 10)° = 180°

⇒ 5x° + 8° + 4x° + 10° = 180°

⇒ 9x° + 18° = 180°

⇒ 9x° = 180° - 18°

⇒ 9x° = 162°

⇒ x° = 162°9\dfrac{162°}{9}

⇒ x° = 18°

So, ∠ A = (5x + 8)°

= (5 ×\times 18 + 8)°

= (90 + 8)°

= 98°

It is given that AD = BC. Therefore, ∠ A = ∠ B

⇒ ∠ B = 98°

Hence, option 1 is the correct option.

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