Developmental Dysplasia of the Hip (DDH) is a medical term represent the hip joint instability that appear mainly in infants. The examination for this condition can be done by ultrasound for children under 6 months old and by X-ray for children over 6 months old. Physician's assessment is based on certain angles derived from those images, namely the Acetabular Angle, and the Center Edge Angle. In this paper, we are presenting a novel, fully automatic algorithm for measuring the diagnostic angles of DDH from the X-ray images. Our algorithm consists of Automatic segmentation and extraction of anatomical landmarks from X-ray images. Both of Acetabular angle and Center edge angle are automatically calculated. The analysis included X-ray images for 16 children recruited for the purposed of this study. The automatically acquired angles accuracy for Acetabular Angle was around 85%, and an absolute deviation of 3.4°±3.3° compared to the physician's manually calculated angle. The results of this method are very promising for the future development of an automatic method for screening X-ray images DDH that complement and aid the physicians' manual methods.