Problem: A quadrilateral is inscribed in a circle. If angles are inscribed in the four arcs cut off by the sides of the quadrilateral, their sum will be:
Answer Choices:
A. 180∘
B. 540∘
C. 360∘
D. 450∘
E. 1080∘
Solution:
∠x=21(a+b+c). Thus the sum of the four angles
S=21(a+b+c+b+c+d+c+d+a+d+a+b)
=23(a+b+c+d)=23⋅360∘=540∘.
