In circle O, PQ = 20, RS = 20, and the measure of arc PT is 35. Find the measure of arc RS.

To find the measure of arc RS, we can use the fact that the measure of an arc is proportional to the length of the arc.

Since PQ = RS, we know that the measure of arc PQ is equal to the measure of arc RS.

Let's assume that the measure of arc RS is x degrees.

According to the given information, the measure of arc PT is 35 degrees.

Since the sum of the measures of arcs PT and PQ is 360 degrees (the total degrees in a circle), we can set up the following equation:

35 degrees + x degrees = 360 degrees

Simplifying the equation, we have:

x degrees = 360 degrees - 35 degrees

x degrees = 325 degrees

Therefore, the measure of arc RS is 325 degrees.

To find the measure of arc RS, we need to use the properties of circles and arcs.

First, let's understand a few key concepts:
1. A circle is a closed curve where all points are equidistant from the center.
2. The length of an arc is directly proportional to the measure of the central angle it subtends. This means that if we know the measure of an angle, we can find the length of the corresponding arc (and vice versa).
3. In a circle, the sum of the measures of the central angles of all the arcs formed by dividing the circle is always 360 degrees.

Now, let's apply these concepts to the given problem:
1. We are given that PQ = 20. This means that arc PQ subtends an angle at the center of the circle. Let's call this angle x.
2. Similarly, RS = 20, so arc RS also subtends an angle at the center of the circle. Let's call this angle y.
3. We are told that the measure of arc PT is 35. Since arc PT is part of the entire circle, its central angle will be 360 degrees minus the sum of the central angles of arcs PQ and RS.
4. Based on the concept mentioned earlier, the sum of the central angles of arcs PQ and RS must be equal to 360 degrees.
5. So, we can write the equation: x + y + 35 = 360.
6. Since we know that arc PQ is 20, we can say x = 20.
7. Substituting the values, we get 20 + y + 35 = 360.
8. Simplifying the equation, we have y + 55 = 360.
9. Subtracting 55 from both sides of the equation, we get y = 305.

Therefore, the measure of arc RS is 305 degrees.

RS is as given...20

(RS=20).