Question

in the given figure, equilateral EBC surmount Square ABCD. find the value x​

Answer 1

Answer:

• x = 45°

Step-by-step explanation:

Given that equilateral triangle EBC surmount square ABCD.

All the sides of equilateral triangle and square are equal and the base of triangle is same as side of square. Therefore,

• AB = BC = CD = AD = CE = BE

We know that all the angles in an equilateral triangle is equal to 60° and all the angles of square are equal to 90°.

Consider ∆ ABE :

It is an equilateral triangle where BE = AB. angle opposite to equal sides are also equal. So, ∠AEB = ∠BAE.

Applying angle sum property of triangle in ∆ ABE :

∠ BAE + ∠ AEB + ABE = 180°

∠ AEB + ∠ AEB + ( 90° + 60° ) = 180°

2 ∠ AEB + 150° = 180°

2 ∠ AEB = 180° - 150°

2 ∠ AEB = 30°

∠ AEB = 15°

Now,

∠ CEB = ∠ CEF + ∠ AEB

60° = x + 15°

60° - 15° = x

45° = x

Therefore value of x is 45°.