Inside the square ABCD, straight lines are drawn through the vertices A and B so that they form an angle

Inside the square ABCD, straight lines are drawn through the vertices A and B so that they form an angle of 15 degrees with the side AB. Prove that the triangle DEC is equilateral, where the point E is the intersection point of the drawn lines.

Consider the triangle ABM.

The angle of the vertex A will be equal to 90 ° – 60 ° = 30 °.

The sides will be equal to AB = AM = a – it is isosceles.

In isosceles triangles, the angles at the base are equal, which means we consider:

Angle AMB = angle ABM = 1/2 (180 ° – angle BAM) = 1/2 (180 ° – 30 °) = 75 °.

Answer: angle AMB = 75 °.