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In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x and choose the option which represents the same.

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100 ∘

90 ∘

80 ∘

70 ∘

answer is A.

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Detailed Solution

Here, we have to calculate the value of x as shown in the diagram above.
So, let us first consider the parallelogram ABDH.
According to the property of a parallelogram, its opposite angles are equal.
So, we have,

∠ A H D = ∠ A B D ∠ A H D = 130 ∘

Now, it can be observed that

∠ A H D

and

∠ D H G

lie on a straight line, and hence form a supplementary pair.
So, we have,

∠ A H D + ∠ D H G = 180 ∘ 130 ∘ + ∠ D H G = 180 ∘ ∠ D H G = 180 ∘ − 130 ∘ ∠ D H G = 50 ∘

Next, if we consider the parallelogram CEFG, we can use the property of adjacent angles being supplementary as follows,

∠ E F G + ∠ F G C = 180 ° 30 ° + ∠ F G C = 180 ° ∠ F G C = 180 ° − 30 ° = 150 ° ∠ F G C = 150 ∘

Now, we can observe that

∠ F G C

and

∠ H G C

lie on a straight line, and hence form a supplementary pair. So, we have,

∠ H G C + ∠ F G C = 180 ∘ ∠ H G C + 150 ∘ = 180 ∘ ∠ H G C = 180 ∘ − 150 ∘ ∠ H G C = 30 ∘

Now, in

△ H G I

, using the angle sum property for the interior angles of a triangle, we get,

∠ I H G + ∠ I G H + ∠ H I G = 180 ° 50 ° + 30 ° + x = 180 ° x = 180 ° − 80 ° x = 100 °

So, the value of x is found to be

100 ∘

.
Hence the correct option is (1).

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