Question

1. Find the measure of angle R.

Answer 1

Answer:

the first option 40 degrees

Step-by-step explanation:

the outward angle at the center of the circle between the two tangential points is 220 degrees.

that means that the inward angle between them is

360 - 220 = 140 degrees.

now consider that there is a triangle between the center of the circle, one of the tangential points (it does not matter which one, as the upper and the lower triangles are equal) and the point R.

we know the angle at the tangential point : 90 degrees by definition (otherwise it would not be a tangent).

and we know the angle at center of the circle, which is half of the inward angle

140 / 2 = 70 degrees.

and at point R we have half of the full angle R.

we can calculate that half by using the fact that the sum of all angles in a triangle is always 180 degrees.

180 = 90 + 70 + R/2

180 = 160 + R/2

20 = R/2

R = 40 degrees