4(x+1) is the only one equal to 0
In this problem, an angle like angle BAC where the
vertices like on the circle itself is called the inscribed angle.
While angle BOC, where O is the center of the circle, is
called the central angle.
Using Proposition III.20 from Euclid's Elements, this is called
the Inscribed Angle Theorem wherein:
∠BOC = 2∠BAC
or ∠BOC / 2 = ∠<span>BAC</span>
The answer you already have selected in the image is correct. Even eyeballing it, you can see that the smaller shape fits into the larger shape 4 times.
We use 2 different rules here:
1) sum of angles in a triangle is equal to 180 degrees
2) when a triangle side is a diameter of the circle, then angle opposite to diameter is equal to 90 degrees.
so from 2) we know that B= 90
then from first one:
sum of angles = 180 = 90 + (3x + 6) + x = 96 + 4x
so 180 - 96 = 4x
so x = 84/4
x = 21
so answer is
A= 3x+ 6 = 63 + 6 = 69
B = 90
C = 21
