In an isosceles triangle ABC with base AC, the outside angle at the apex C is 123 ° Find the angle BAC.

Outside angle at apex C – angle ВСD = 123 degrees. The BCD angle and the BCA angle are adjacent angles. Adjacent corners are a pair of corners that have one vertex in common and one side in common, together they make up a flat angle that is 180 degrees. Thus, the sum of adjacent angles is 180 degrees:
BCD angle + BCA angle = 180 degrees; 123 degrees + BCA angle = 180 degrees; ICA angle = 180 degrees – 123 degrees; ICA angle = 57 degrees.
Since, according to the condition, AC is the base, then the angle BAC = the angle of the BCA (the angles at the base are equal), therefore the angle BAC = 57 degrees.
Answer: angle BAC = 57 degrees.