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

Answer:

105 degrees.

Step-by-step 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.

$\angle ACB=\dfrac{\angle BCD}{2}=\dfrac{90^\circ}{2}=45^\circ$

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.