Question

in the circle below, the measure of arc qt is 43 and the measure of angle p is 5. what is the measure of arc rs?

Explanation:

Step1: Recall the secant - secant angle formula

The measure of the angle formed by two secants intersecting outside a circle is given by $\angle P=\frac{1}{2}(\text{measure of arc }RS-\text{measure of arc }QT)$.

Step2: Substitute the given values

We know that $\angle P = 5$ and $\text{measure of arc }QT=43$. Substituting into the formula $5=\frac{1}{2}(x - 43)$, where $x$ is the measure of arc $RS$.

Step3: Solve for $x$

First, multiply both sides of the equation by 2: $2\times5=x - 43$. So, $10=x - 43$. Then add 43 to both sides: $x=10 + 43$.

Answer:

53