Question

In a circle where m∠vbc=(3x+4)∘ , what is the value of x if ∠vbc measures 90 degrees?

a) 28
b) 32
c) 25
d) 22

Answer 1

The value of x in the given circle can be found by setting up an equation using the measure of angle VBC and the circumference of the circle.

Step-by-step explanation:

In a circle, the measure of an angle formed by two points on the circumference and the center is half the measure of the arc it intercepts. Since angle VBC is 90 degrees, its intercepted arc also measures 90 degrees. Therefore, 90 degrees is half the measure of the entire circumference of the circle. The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. So if the entire measure of the circumference is 90 degrees, we can set up the equation 90 = (2πr)/2, which simplifies to 90 = πr. To find the value of x, we need to determine the value of r using the equation 90 = πr.