Question

In Figure an equilateral triangle EAB surmounts the square ABCD. Find the value of X and y

Answer 1

The concept:

Equilateral triangles are equi angular.

Each angle of equilateral triangle is 60°.

So

x + <1 = 60°       .......(!)

<2 = 60°

Now ABCD is a square

So <3 = 90°

Hence <2 + <3 = 60° + 90° = 150°

Also all sides of triangle & square are equal

Now in triangle EBC

EB = BC

so <1 = <y

Now <1 + y + 150° = 180°

y + y = 30°

2y= 30°

y=15°

Hence <1 = 15°

But x + <1 = 60°

So x + 15° = 60°

x = 45°

The value of x = 45° & the value of y = 15°.

Answer 2

The concept:

Equilateral triangles are equi angular.

Each angle of equilateral triangle is 60°.

So

x + <1 = 60°       .......(!)

<2 = 60°

Now ABCD is a square

So <3 = 90°

Hence <2 + <3 = 60° + 90° = 150°

Also all sides of triangle & square are equal

Now in triangle EBC

EB = BC

so <1 = <y

Now <1 + y + 150° = 180°

y + y = 30°

2y= 30°

y=15°

Hence <1 = 15°

But x + <1 = 60°

So x + 15° = 60°

x = 45°

The value of x = 45° & the value of y =15.