Question

ABCD is a square. ABE is an equilateral triangle. x = ???

Answer 1

All the sides of a square must equal 90 degrees. With that information, we can determine that corner C is 45 degrees. We can tell that the line that reaches corner C divides the angle by 2. So 90/2=45.

We also know

Answer 2

105 degrees.

Explanation:

Given information: ABCD is a square. ABE is an equilateral.

To find : The value of x.

We know that the measure of each interior angle of a square is 90 degrees and the measure of each interior angle of an equilateral triangle is 60 degrees.

`\angle ABC=90^\circ`

`\angle ABE=60^\circ`

`\angle EBC=\angle ABC-\angle ABE=90^\circ -60^\circ=30^\circ`

Diagonals of a square divide the interior angles in two equal parts.

`\angle ACB=(\angle BCD)/(2)=(90^\circ)/(2)=45^\circ`

We know that sum of interior angles of a triangle is 180 degrees.

`\angle EBC+\angle ACB+x=180^\circ`

`30^\circ+45^\circ+x=180^\circ`

`75^\circ+x=180^\circ`

`x=180^\circ-75^\circ`

`x=105^\circ`

Therefore, the value of x is 105 degrees.