in order to receive an accurate diagnosis and treatment planning , many researchers have used different criteria to determine the anterior - posterior relationship of the jaws .
although molar relationship has been used in angel classification , it is clear that canine and molar relationship indicates the anterior - posterior relationship of the jaws when teeth are placed in the accurate position on the dental arch .
using plaster models for classification of malocclusion or determination of the jaws relationship , without lateral cephalometric radiograph is not reliable , particularly for patients who have defective dental structures .
currently , several types of intracranial plans have been used as reference lines to determine discrepancy of the jaws .
the most popular measurement of discrepancy of the jaws in anterior - posterior dimension is a point , nasion , b point ( anb ) angle , which indicates the relationship of apical base of maxilla to mandible .
based on the geometric studies ( studies conducted geometrically rather than statistically ) , following factors are able to change anb angle , without any effect on the anterior - posterior relationship of apical bases : rotation of the jaws around anterior cranial base.rotation of the occlusal plane around anterior cranial base , with or without jaws rotation.position of nasion in the sagittal and vertical dimension and the length of anterior cranial base ( s - n).facial height.rotation of s - n plan .
rotation of the occlusal plane around anterior cranial base , with or without jaws rotation .
position of nasion in the sagittal and vertical dimension and the length of anterior cranial base ( s - n ) .
thus , regarding the geometric studies , anb angle can not always indicate anterior - posterior relationship of the jaws accurately .
this index is a linear measurement , which is the distance between two perpendicular lines from points a to b to functional occlusal plane .
geometric studies have shown that the value of wits appraisal index may be influenced by alteration of functional occlusal plane and vertical distance of points a and b as well as sagittal alteration of points a and b. some researchers have offered linear and angular measurements based on palatal plane . although this plane is constant , with increasing of age , it has variable gradient , so it is difficult to determine normal average .
as these indexes are influenced by anatomic landmarks and dental occlusion and regarding to probability of effect of these landmarks on accuracy of evaluations , it is necessary to access an independent index .
recently ,  and  angles have been introduced , which are not dependent on cranial landmarks or dental occlusion .
therefore , they are reliable indexes in cases that previous indexes such as anb angle and wits appraisal may not be used .  angle is a novel method of measurement of skeletal discrepancy between the maxilla and mandible in sagittal plan .
this angle uses three anatomic landmarks : point a , point b and mandibular plan : point a : is the deepest point on the midline of the maxilla , which moves from base to alveolar process .
point b : is the most anterior part of base of the mandible and the most posterior point of the outer contour of mandibular alveolar process in midline .
 angle is the angle between ab line and perpendicular line from a to mandibular plan [ figure 1 ] .
 angle also uses three anatomic landmarks : point a , point b and condylar axis : point c ( condylion ) : is the most posterior - superior point on condylar head of the mandible ( in the present study , c is considered as the center of the condyle ) .
 angle is the angle between ab line and perpendicular line from point a to cb line [ figure 2 ] . considering ethnical , sexual and growth differences , it is necessary to evaluate normal cephalometric average of every population .
the aim of this study was to evaluate and to compare the range of  and  angles of 6 - 17-year - old children of isfahan who have normal occlusion .
this is a descriptive  analytical study . in order to conduct this study , archive documents of orthodontic department of isfahan dental school
a total of 235 cephalometric radiographs of children , who had no history of orthodontic treatment and also based on 13 following criteria categorized as normal occlusion , were selected : symmetric face.having the whole teeth regarding to age ( lack of primary tooth was acceptable if there was adequate space).normal tooth form , position and size.class i molar relationship for permanent tooth ( class i molar relationship or end to end relationship during mixed dentition or flush terminal plane relationship of second primary teeth [ e ] in cases of incomplete growth of permanent first molar).class i canine relationship.proper overbite up to 3 mm and over jet up to 2 mm.slight or no space between teeth.slight or no dental rotation.slight or no dental crowding.no posterior cross bite.no history of previous orthodontic treatment.no history of orthognathic surgery.no congenital disorder . having the whole teeth regarding to age ( lack of primary tooth was acceptable if there was adequate space ) .
class i molar relationship for permanent tooth ( class i molar relationship or end to end relationship during mixed dentition or flush terminal plane relationship of second primary teeth [ e ] in cases of incomplete growth of permanent first molar ) .
acetate tracing paper ( dentaurum , germany ) was used for tracing and cephalometric protractor ( 3 m unitek , corporation , monrovia , california , usa ) with accuracy of 1 was used for measurement .
anb angle , wits appraisal index ,  and  angles were measured . during measurement
, 16 subjects were excluded due to clear inconsistency between anb angle and wits appraisal index .
furthermore , 17 subjects were excluded due to failure of determination of condylar center position in order to measure  angle .
three subjects were excluded due to superimposition of right and left mandibular plan and consequently failure of determination of  angle . finally , 199 subjects ( 112 females and 87 males ) participated in this study .
correlations of  and  angles with anb angle and wits appraisal index were determined using pearson correlation coefficient .
t - test was used to determine the relationship between gender and  and  angles and anova was used to evaluate the relationship between age groups and  and  angles ( p < 0.05 ) .
frequency of 6 - 17-year - old children of isfahan with normal occlusion based on age group mean and standard deviation of  and  angles are illustrated in table 2 .
mean and standard deviation of anb angle , wits appraisal ,  and  angles in 6 - 17-year - old children of isfahan with normal occlusion according to t - test , there was a significant difference between the mean of  angle and gender .
however , there was no significant difference between other angles and gender [ table 3 ] .
there was significant differences between the mean of  angle and 14 - 17-year - old age group ( p = 0.01 ) while the mean of  angle showed a significant difference in age groups of 8 - 10-year - old ( p = 0.02 ) and 14 - 17-year - old ( p = 0.02 ) .
comparison mean and standard deviation of anb angle , wits appraisal ,  and  angles in 6 - 17-year - old children of isfahan with normal occlusion based on sex according to spearmen correlation coefficient there was no significant relationship between  angle and age ( p = 0.054 ) ( r = 0.138 ) , while there was a direct , significant relationship between  angle and age ( r = 0.435 ) .
the relationship between values of  and  angles and anb angle are presented on diagrams 1 and 2 and the relationship between these angles with wits appraisal index is presented on diagrams 3 and 4 .
relationship of  angle with a point , nasion , b point angle relationship of  angle with a point , nasion , b point angle relationship of  angle with wits appraisal index relationship of  angle with wits appraisal index
accurate measurement of anterior - posterior relationship of the jaws has a major importance in orthodontic treatment plan .
the well - known criterion to investigate the anterior - posterior relationship of the jaws is anb angle .
a common alternative is wits appraisal index , which is not dependent on cranial landmarks or jaws rotation ; however , accurate diagnosis of functional occlusal plane is difficult and it may occur after orthodontic treatments due to alteration of functional occlusal plane rather than alteration of sagittal relationship of the jaws . in order to compensate the deficiency of anb angle and wits appraisal index , baik and ververidou suggested  angle .
the researchers claimed that  angle not only is independent of cranial landmarks and functional occlusal plane , but also it seems that clockwise or counter - clockwise rotation of the jaws has slight influence on this angle .
another advantage of  angle is that it can be applied in serial evaluation of orthodontics treatment plan and shows changes in sagittal relationship of the jaws related to growth and orthodontic or orthognathic interference .
in addition , it can be used as accurate criteria in orthognathic surgery for patients with anterior - posterior and vertical skeletal disorder .
however , major disadvantage of this angle is determination of condylar center , which is not always easy .
this issue has been similarly experienced in the present study , which 17 subjects were excluded due to lack of clarity of condylar area . in order to obtain accurate measurement of  angle , cephalometric
radiographs must have high quality , so that the clinician can easily trace posterior border of ramus and determine condylar head position .
the advantage of using the center of condyle rather than condylion point is that accurate tracing of condylar contour is not usually easy .
as it is illustrate in figure 2 , if real condylar center is point c , but clinician locates it in a circle with a radius of 2 mm ,  angle is affected less than 1 , which makes its application more acceptable . in the present study ,
baik and ververidou showed the range of  angle 27.5 - 43.5 and 27 - 35 respectively .
the difference between these studies is probably due to different sample size , inclusion criteria and demographic features of patients .
the mean of  angle was 31.7  3.3 in the current study , which is consistent with the results of fattahi et al .
suggested  angle , which is superior to  angle because the determination of mandibular plane is easier and the quality of radiograph does not influence this plane .
however , mandibular plane may be defective in some lateral cephalograms due to weak radiographic technique .
one of the advantages of  angle is that the rotation of the lower jaw from temporomandibular joint area or the rotation of mandibular body does not really influence the  angle as a and b points change their position .
however , if mandibular plane changes without displacement of a and b points , the angle will be failed . in the present study ,
the range of  angle was 8 - 27 , while fattahi et al . showed 11 - 29 .
the mean value of  angle was 17.34  3.74 , which is consistent with the results of fattahi et al .
according to spearman correlation coefficient there was direct significant , but weak relationship between  angle and age ( r = 0.435 ) .
as  angle increases with the increase of age , it can be suggested that  angle is consistent with cephalocaudal gradient of the growth curve .
pearson correlation coefficient revealed that there was reverse significant relationship between anb angle and  angle ( r = 0.520 ) and also  angle ( r = 0.329 ) .
as an increase in  angle and  angle indicated a tendency to class iii and a decrease in anb angle indicates the same tendency , these angles reinforce each other in the classification of the malocclusion .
there was also weak and reverse significant relationship between wits appraisal index and  angle ( r = 0.412 ) and  angle ( r = 0.427 ) .
as increase of these angles and a decrease of wits appraisal index ( more negative ) indicate tendency to c1ass iii , both of them reinforce each other in the classification of the malocclusion .
biak and ververidou suggested that there is a significant relationship between anb angle and wits appraisal index and  angle . according to the present study
, there was a direct significant relationship between  angle and  angle ( r = 0.621 ) .
therefore , it can be said that these two angles have consistent validity and can be well used in the determination of anterior - posterior malocclusion .
in fact , all linear and angular measurement in lateral radiographies has specific advantages and disadvantages , thus none of the methods can be used merely as an accurate method for diagnosis and treatment plan in orthodontics . although  angle and  angle are able to diagnosis the anterior - posterior relationship of the jaws and bone disorder , previous cephalometric measurements should not be ignored .
based on the findings of the current study , further studies on the sensitivity and specificity of  angle and  angle in three types of malocclusion and also comparison of these angles with other method of measuring jaw relationship such as the angle of convexity and facial angle are recommended .
considering that  angle and  angle do not have the disadvantages of previous measurements such as anb angle and wits appraisal index for evaluation of anterior - posterior relationship of the jaws , they may be an accurate method for diagnosis of jaw disorders and treatment plan .
 background : linear and angular measurements such as a point , nasion , b point ( anb ) angle and wits appraisal index are not accurate enough to evaluate sagittal relationship of the jaws . 
 the aim of this study was to evaluate and compare the range of  and  angles in 6 - 17-year - old children of isfahan , having normal occlusion.materials and methods : this was an analytical descriptive study . 
 for this study , 235 cephalometric radiographs of patients who did nt receive orthodontics treatments and based on 13 indexes had normal occlusion , were selected . 
 after tracing of cephalograms , anb angle , wits appraisal index ,  angle ( resulted from the intersection of ab line and perpendicular line from point a to mandibular plane ) and  angle ( resulted from the intersection of ab line and perpendicular line from point a on cb line ) were measured . 
 data was analyzed by t - test , anova and pierson - spearman correlation coefficient ( p < 0.05).results : mean value of  and  angles were 17.34  3.47 and 31.7  3.31 and ranged from 8 - 27 to 21.5 - 39 respectively . according to t - test 
 , there was a significant difference between two sex groups for  angle ( p = 0.02 ) ; however , it was not significant for  angle . 
 according to spearman correlation coefficient , there was no significant difference between age and  angle ; however ,  angle was directly and significantly related to age ( r = 0.435 ) . 
 there was significant and reverse relationship between  and  angles with anb angle and wits appraisal index.conclusion: and  angles are reliable and can be used to evaluate the anterior - posterior relationship of the jaws . 
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
CONCLUSION