4.2. Exterior Angles Theorems http://www.ck12.org
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◦.
x+p= 180 ◦
120 ◦+p= 180 ◦
p= 60 ◦Watch this video for help with the Examples above.
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Click image to the left for more content.CK-12 Foundation: Chapter4TriangleSumTheoremA
Concept Problem Revisited
The third exterior angle of the triangle below is^6 1.
By the Exterior Angle Sum Theorem:
m^61 + 130 ◦+ 130 ◦= 360 ◦
m^61 = 100 ◦