Supplementary angles

Supplementary angles.

Two angles are supplementary angles if they add up to 180°.

• An angle is or has Supplementary if he's younger than 180 {displaystyle 180^{circ}}.

• The value of 180 {displaystyle 180^{circ}} is the same as two straight angles, π π {displaystyle pi } rad or 200g{displaystyle 200^{g}} Hundreds.
• An angle supplement is what is missing to the angle to measure a flat or flat angle.

Getting method

Arithmetic

To get the extra angle β β {displaystyle beta } of a certain angle α α {displaystyle alpha }It will be restored α α {displaystyle alpha } a 180 {displaystyle 180^{circ}}, so:

β β =180 − − α α {displaystyle beta =180^{circ }-alpha }

Properties

• If two angles are additional to two other congruent angles, they are also congruent with each other.
• The sinuses of the extra angles are the same, for example:

sen α α =sen (180 − − α α ){displaystyle operatorname {sen} alpha =operatorname {sen}(180^{circ }-alpha)}}

sen α α =sen (π π − − α α ){displaystyle operatorname {sen} alpha =operatorname {sen}(pi -alpha)}}

sen 120 =sen 60 {displaystyle operatorname {sen} 120^{circ }=operatorname {sen 60}{circ }}}

• The extra angles are of equal absolute value, but of an inverse sign, as the following examples show:

# α α =− − # (180 − − α α ){displaystyle cos alpha =-cos(180^{circ }-alpha)}}

# α α =− − # (π π − − α α ){displaystyle cos alpha =-cos(pi -alpha)}

# 120 =− − # 60 {displaystyle cos 120^{circ }=-cos 60^{circ }}}