Question

In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.

Answer 1

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°