Find the value of  as shown in the figure below.
A)0.01
B)0.02
C)0.04
D)0.05

Question

Find the value of &#61537; as shown in the figure below.
A)0.01 
B)0.02 
C)0.04 
D)0.05

Quizplus · Accepted Answer

The angle at the center of the circle is twice the angle at the circumference for the same arc. Thus, the angle at the center must be 120°, which means the arc it subtends has a measure of (120/360) * 2πr = (1/3)πr. Similarly, the arc subtended by the inscribed angle (with measure x) is (x/360) * 2πr. Since these two arcs add up to the entire circumference of 2πr, we have:

(x/360) * 2πr + (1/3)πr = 2πr
Simplifying and solving for x, we get:
x/360 = (2/3) - (1/6)
x/360 = (1/2)
x = 180
Therefore, the inscribed angle has a measure of 180°, which means it subtends an arc of half the circumference. Thus, the length of the arc (in relation to the entire circumference) is 1/2, which means the value of % is 0.02 or 2%. The answer is B.

Find the Value of  as Shown in the Figure