Question

BEC is an equilateral triangle in the square ABCD. Find the value of x in the figure.

Answer 1

Explanation:

OBC= 45°( diagonal segment)

BCO= 60° (Since BEC is an equilateral ∆)

So in ∆OBC,

=> OBC-BCO+X= 180°

=> X=180°-60°-45°

=> X= 75°

Hope it will be helpful ☺️ thank you!!

Answer 2

Given :

BEC is an equilateral triangle in the square ABCD.

To find :

Value of x in the given figure.

Solution :

In triangle BEC , ∠ EBC = ∠ BCE = 60°

( The measure of three angles of equilateral triangle is 60°)

In triangle EBC ∠ CBD = 45°.

{ ABCD is a square, all angles of a square are right angles .

BD is a diagonal , BD bisects the ∠ ABC .

hence ∠ABD = ∠ CBD = 45° .}

In triangle FBC ,

∠ FBC + ∠ FCB + ∠CFB = 180°

( sum of angles of a triangle is 180°. )

45° + 60° + x = 180°

105 ° + x = 180°

x = 180° - 105°

x = 75°

Hence x = 75°.