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Mathematics

In the given figure ABCD is a parallelogram, angles DAB and ABC are in the ratio 5 : 7, the value of x is:

In the given figure ABCD is a parallelogram, angles DAB and ABC are in the ratio 5 : 7, the value of x is: Special Types of Quadrilaterals, Concise Mathematics Solutions ICSE Class 8.

  1. 105°

  2. 85°

  3. 75°

  4. none of these

Quadrilaterals

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Answer

As we know that the consecutive angles of a parallelogram are supplementary.

Let ∠DAB = 5a and ∠ABC = 7a.

Since consecutive angles are supplementary:

⇒ ∠DAB + ∠ABC = 180°

⇒ 5a + 7a = 180°

⇒ 12a = 180°

⇒ a = 180°12\dfrac{180°}{12}

⇒ a = 15°

Then,

∠ABC = 7a = 7 ×\times 15° = 105°

The other angle x,

x + ∠ABC = 180°

⇒ x + 105° = 180°

⇒ x = 180° - 105°

⇒ x = 75°

Hence, option 3 is the correct option.

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