Problem: In the adjoining figure ∠E=40∘ and arcAB,arcBC and arcCD all have equal length. Find the measure of ∠ACD.
Answer Choices:
A. 10∘
B. 15∘
C. 20∘
D. (245)∘
E. 30∘
Solution:
Let AB=x∘ and AD=y∘. Then
3x+y21(x−y)=360=40.
Doubling both sides of the second equation and adding the resulting equation to the first equation yields x=110 and ∠C=15∘.
