Question

Quadrilateral ABCD is inscribed in circle P as shown. Which statement is necessarily true?
m∠A+m∠B=m∠C+m∠D

m∠A+m∠C=m∠B+m∠D

m∠A+m∠D=m∠B+m∠Cm∠A+m∠D=m∠B+m∠C

m∠A+m∠B=2(m∠C+m∠D)

Answer 1

@phi

Answer 2

Is it B? @phi

Answer 3

yes

Answer 4

Thanks How do I give you a medal

Answer 5

we can show it must be true that
<A + <C = <B + <D
using the idea that each of these "inscribed angles" are 1/2 of the intercepted arcs
<A + <C together will intercept the entire circle (making their sum 1/2 of 360= 180)
and ditto for <B + <D