Question

In the given figure ABCD is a rhombus if angle A = 72 degree find the value of x

Answer 1

Answer:

One property of a rhombus states that:-

The base angles should be supplementary i.e. equal to 180 degrees. And every opposite angle should be equal to each other.

∠A = 72°

∠A + ∠B = 180° [base angles]

72° + ∠B = 180°

∠B = 180 - 72

∠B = 108°

Now, we can notice that line DB is acting as a line of symmetry and dividing ∠B into two equal parts. 'X' is half of ∠B.

$\frac{B}{2} = x$

$\frac{108}{2} = x$

$54 = x$

The value of 'x' = 54°

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