Question

The central angle of arc is 70 degrees and the inscribed angle is 35 degrees. What is the measure of the circumscribed angle?

Answer 1

In a circle, there is a relationship between the central angle, the inscribed angle, and the circumscribed angle. The relationship is as follows:

The central angle (θ) is twice the measure of the inscribed angle (α) that subtends the same arc:

θ = 2α

Given that the inscribed angle is 35 degrees, we can find the central angle:

θ = 2 * α = 2 * 35 degrees = 70 degrees

The circumscribed angle (β) is twice the measure of the central angle:

β = 2θ

Now that we know the central angle is 70 degrees, we can find the circumscribed angle:

β = 2 * θ = 2 * 70 degrees = 140 degrees

So, the measure of the circumscribed angle is 140 degrees.