Answer:
131 degrees
Step-by-step explanation:
When you take all parts of the circle and add them up, you are given 31y-12.
When you set 31y-12 to 360 (31y-12=360), you can solve for y and plug it in to all variables of the circle.
31y-12=360
Add 12 to both sides to cancel it out from the left.
31y=372
Divide 31 on both sides to cancel out and leave y on the left.
y=372/31
y=12
Now, plug 12 in to each variable. 54+77=131 degrees
131 degrees is the arc measure of minor arc \stackrel{\large{\frown}}{BC} BC ⌢ B, C, start superscript, \frown, end superscript.
200°
The only angle we are given is Angle BAC. Since it is an inscribed angle, its measure is half that of the arc it cuts off. Arc BC therefore must have twice the measure of Angle BAC, so arc BC = 200°. Because there are 360 degrees in a circle, Arc BC + arc BAC = 360°.
O is the center of the circle. ∠ACB= ∠ADB. So, angle BAC and BDC have the same arc Bc in the circumference, these angles must be congruent. So, angle BDC is equal to 56 degrees.
Learn more about the arc measure at
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