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Question
In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.
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Solution
We have, two parallelograms ABDH and CEFG.
Now, In ABDH,
∴ ∠ABD = ∠AHD = 130° ...[∵ Opposite angles of a parallelogram are equal]
And ∠GHD = 180° – ∠AHD
= 180° – 130° ...[Linear pair]
⇒ ∠GHO = 50°
Also, ∠EFG + ∠FGC = 180° ...[∵ Adjacent angles of a parallelogram are supplementary]
⇒ 30° + ∠FGC = 180°
⇒ ∠FGC = 180° – 30° = 150°
And ∠HGC + ∠FGC = 180° ...[Linear pair]
∠HGC = 180° – ∠FGC
= 180° – 150°
∴ ∠HGO = 30°
In ΔHGO, by using angle sum property,
∠OHG + ∠HGO + ∠HOG = 180°
⇒ 50° + 30° + x = 180°
⇒ x = 180° – 80°
= 100°
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