
If D lies in the interior of ∠ABC, then
m∠ABD + m∠DBC = m∠ABC. 
This concept may also be referred to as
"whole quantity" or "the whole is equal to the sum of its parts." 


An angle bisector is a ray from the vertex of the angle into the interior of the angle forming two congruent angles.





Remember that the word "bisect" means to cut into two equal pieces. 
Angles Forming a Straight Line 
If the nonshared sides of two, or more, adjacent angles form a straight line, the measures of the angles add up to 180º.



m∠1 + m∠2 + m∠3 = 180º

This is a "common sense" rule. A straight line is also a straight angle, which contains 180º. If these angles are adjacent (don't overlap), and their nonshared sides form a straight line, the angles comprise a straight angle which contains 180º. 
If two, or more, adjacent angles completely surround a point, the measures of the angles add up to 360º.



m∠1 + m∠2 + m∠3 = 360º

This is also a "common sense" rule. The complete revolution around a point is a circular 360º. You might also think of it as two straight lines (straight angles). If these angles are adjacent (don't overlap), and together they form one complete revolution, the measures of the angles will total 360º. 
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