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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