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

**Solution:**

Given, ABDH and CEFG are two __parallelograms__.

We have to find the value of x.

Considering parallelogram ABDH,

Given, ∠ABD = 130°

We know that the opposite angles of a parallelogram are equal.

∠ABD = ∠AHD

So, ∠AHD = 130°

We know that the __linear pair of angles__ are supplementary.

∠AHD + ∠GHD = 180°

130° + ∠GHD = 180°

∠GHD = 180° - 130°

∠GHD = 50°

We know that the __adjacent angles__ of a parallelogram are supplementary.

∠EFG + ∠FGC = 180°

Given, ∠EFG = 30°

30° + ∠FGC = 180°

∠FGC = 180° - 30°

∠FGC = 150°

We know that the linear pair of angles are supplementary.

∠HGC + ∠FGC = 180°

∠HGC + 150° = 180°

∠HGC = 180° - 150°

∠GHD = 30°

In triangle HGO,

By __angle sum property__ of a triangle,

∠OHG + ∠HGO + ∠HOG = 180°

50° + 30° + x = 180°

80° + x = 180°

x = 180° - 80°

Therefore, the value of x = 100°.

**✦ Try This:** A piece of land is in the shape of a rhombus ABCD in which each side measures 180 m and diagonal AC is 120 m long. Find the area of the rhombus.

**☛ Also Check: **NCERT Solutions for Class 8 Maths

**NCERT Exemplar Class 8 Maths Chapter 5 Problem 157**

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

**Summary:**

ABDH and CEFG are two parallelograms. The value of x is 100°.

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