Question

In the following figure of a ship , ABDH and CEFG are two parallelogram s. Find the

value of x.​

Answer 1

x in the parallelogram is the opposite angle

Answer 2

Given:

• ABDH and CEFG are parallelograms
• ∠ABD = 130°
• ∠EFG = 30°

To find:

• The value of x

Solution:

Let us first find the measure of the angle D of parallelogram ABDH.

∠HDB + ∠ABD = 180 because adjacent sides of a parallelogram are supplementary.

⇒ ∠HDB + 130 = 180

⇒ ∠HDB = 180 - 130

⇒ ∠HDB = 50°

Now, let us find the measure of angle C of parallelogram CEFG.

∠GCE = ∠EFG since opposite angles in a parallelogram are equal.

⇒ ∠GCE = 30°

Why did we find the measures of ∠C and ∠D? Because ∠x, ∠C and ∠D form a triangle. By the angle sum property of triangles, the sum of ∠x, ∠C and ∠D will be equal to 180°.

⇒ ∠x + ∠C + ∠D = 180

⇒  ∠x + 30 + 50 = 180

⇒  ∠x + 80 = 180

⇒  ∠x = 180 - 80

⇒ ∠x = 100

Hence, the value of x is 100°.