http://www.ck12.org Chapter 4. Triangles and Congruence
Solution:
m^61 + 92 ◦= 180 ◦by the Linear Pair Postulate, som^61 = 88 ◦.
m^62 + 123 ◦= 180 ◦by the Linear Pair Postulate, som^62 = 57 ◦.
m^61 +m^62 +m^63 = 180 ◦by the Triangle Sum Theorem, so 88◦+ 57 ◦+m^63 = 180 ◦andm^63 = 35 ◦.
m^63 +m^64 = 180 ◦by the Linear Pair Postulate, som^64 = 145 ◦.
Looking at Example 5, the exterior angles are 92◦, 123 ◦, and 145◦. If we add these angles together, we get 92◦+
123 ◦+ 145 ◦= 360 ◦. This is always true for any set of exterior angles for any polygon.
Exterior Angle Sum Theorem:Each set of exterior angles of a polygon add up to 360◦.
m^61 +m^62 +m^63 = 360 ◦
m^64 +m^65 +m^66 = 360 ◦We will prove this theorem for triangles in the review questions and will prove it for all polygons later in this text.
Example 6:What is the value ofpin the triangle below?
Solution:First, we need to find the missing exterior angle, we will call itx. Set up an equation using the Exterior
Angle Sum Theorem.