4.2. Exterior Angles Theorems http://www.ck12.org
6 4 ∼= (^67)
6 5 ∼= (^68)
6 6 ∼= (^69)
Example B
Find the measure of the numbered interior and exterior angles in the triangle.
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 ◦.
Example C
What is the value ofpin the triangle below?
First, we need to find the missing exterior angle, we will call itx. Set up an equation using the Exterior Angle Sum
Theorem.
130 ◦+ 110 ◦+x= 360 ◦
x= 360 ◦− 130 ◦− 110 ◦
x= 120 ◦
xandpare supplementary and add up to 180◦.