In an isosceles triangle abc on the base ac points d and e are marked so that ce = ad, angle bdc = 110 degrees. Find the corner bea.

Let’s consider a triangle abc. Since it is isosceles, then ab = bc, and the angles at the base are equal: <bac = <bca.
Now consider the two triangles ade and ecb. These triangles are equal because they are equal: ab = bc, ad = ec, <bac = <bca. So bd = be, <bde = <bed.
But the angle <bdc = 110 (degrees) by condition. So, <bdc = <bed = 110, that is, two angles in the triangle bde are equal to 110 degrees. And this is not possible, since all the angles in the triangle add up to only 180 degrees. And so, according to the solution, it was found that the desired angle <bea = <bed = <bde.
This means that the angle in the data should be less than 90 degrees. And what is the desired angle found – given angle bdc.