In the opposite figure : m arc (AC) = m arc (AD ) = 2 m arc (BD) , m arc (BC) = 100° , then θ = .⁰

(a) 78
(b) 65
(c) 52
(d) 84

  (a) 78

Step-by-step explanation:

The sum of arcs of a circle is 360°. The measure of θ is the average of the measures of arcs BD and AC.

  AC +AD +BD +100 = 360

  (2BD) +(2BD) + BD = 260 . . . . use the given relation for AC, AD; subtract 100

  BD = 52 . . . . . . . . . . . . . . . . . divide by 5

  θ = (AC +BD)/2 = (2(52) +52)/2 = 52 +26

  θ = 78 . . . . degrees