11.4 More About Angles

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Def. Vertical Angles—pairs of angles such as angles 1 and 3 or 2 and 4.

 

 

 

 

 

 

 

 

 

 

 

 

Def. Supplementary Angles—two angles whose sum of measures is 180°.

 

 

 

 

 

 

 

 

 

Def. Complementary Angles—two angles whose sum of measures is 90°.

 

 

 

 

 

 

Def. Transversal—any line that intersects a pair of lines.

 

 

 

 

 

 

 

 

 

 


 

 

Interior Angles: Angles 2, 4, 5, 6

 

Exterior Angles: Angles 1, 3 7, 8

 

Alternate Interior Angles: Angles 2 & 5; 4 & 6

 

Alternate Exterior Angles: Angles 1 & 7; 3 & 8

 

Corresponding Angles: Angles 1 & 2; 3 & 4; 5 & 7, 6 & 8

 

 

 

T.11.3 If any two distinct coplanar lines are cut by a transversal, then a pair of corresponding angles, alternate interior or exterior angles are congruent if and only if the lines are parallel.

 

 

 

 

 

 

 

 

 

 

 

 


Sum of the measures of the interior angles of a triangle:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


T. 11.4 The sum of the measures of the interior angles of a triangle is 180°.

 

T. 11.5 The sum of the measures of the exterior angles of a convex polygon is 360°.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T. 11.6 a) The sum of the measures of the interior angles of any convex polygon with n sides is 180n – 360 or (n – 2)180.

 

 

b) The measure of a single interior angle of a regular n-gon is .