http://www.ck12.org Chapter 4. Triangles and Congruence
Solution: 4 ABCto the left is an example of an equiangular triangle, where all three angles are equal. Write an
equation.
m^6 A+m^6 B+m^6 C= 180 ◦
m^6 A+m^6 A+m^6 A= 180 ◦
3 m^6 A= 180 ◦
m^6 A= 60 ◦Ifm^6 A= 60 ◦, thenm^6 B= 60 ◦andm^6 C= 60 ◦.
Theorem 4-1:Each angle in an equiangular triangle measures 60◦.
Example 3:Find the measure of the missing angle.
Solution:m^6 O= 41 ◦andm^6 G= 90 ◦because it is a right angle.
m^6 D+m^6 O+m^6 G= 180 ◦
m^6 D+ 41 ◦+ 90 ◦= 180 ◦
m^6 D+ 41 ◦= 90 ◦
m^6 D= 49 ◦Notice thatm^6 D+m^6 O= 90 ◦because^6 Gis a right angle.
Theorem 4-2:The acute angles in a right triangle are always complementary.
Exterior Angles
Exterior Angle:The angle formed by one side of a polygon and the extension of the adjacent side.
In all polygons, there aretwosets of exterior angles, one going around the polygon clockwise and the other goes
around the polygon counterclockwise.
By the definition, the interior angle and its adjacent exterior angle form a linear pair.