Problem:
β 1+β 2=180β.
β 3=β 4.
Find β 4.
Answer Choices:
A. 20β
B. 25β
C. 30β
D. 35β
E. 40β
Solution:
Since the sum of the angles of a triangle is 180β,40β+70β+β 1= 180β and β 1=70β. This means that β 2=110β. Then 110β+β 3+β 4=180β, so β 3+β 4=70β and β 3=β 4=35β.
Answer: Dβ.
The problems on this page are the property of the MAA's American Mathematics Competitions