Consider the given diagram. Let's mark the measure of RT as x^(∘) and the measure of ST as y^(∘).
We will start by finding the measure of arc ST and then use it to find the measure of RT. Let's do those things one at a time.
Finding mST
Consider the diagram once again.
The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Therefore, 55^(∘) is half of y^(∘).
55=1/2y ⇔ y=110
Therefore, we have found that the arc ST measures 110^(∘).
Finding mRT
Let's add the obtained information to our diagram.
Since the measure of a full turn around a circle is 360^(∘), we can use the Arc Addition Postulate to find the measure of RT. Let's write an equation in terms of x and solve it!
