Question

question 2 of 22
in the diagram below, m\\(\widehat{pr}\\) = 140° and m\\(\widehat{qs}\\) = 106°. what is the measure of ∠ptr?
a. 140°

Explanation:

Step1: Recall angle - arc relationship

The measure of an angle formed by two intersecting chords in a circle is given by $\frac{1}{2}$ the sum of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The intercepted arcs for $\angle PTR$ are $\widehat{PR}$ and $\widehat{QS}$. We are given that $m\widehat{PR}=140^{\circ}$ and $m\widehat{QS} = 106^{\circ}$.

Step3: Apply the formula

$m\angle PTR=\frac{1}{2}(m\widehat{PR}+m\widehat{QS})$. Substitute the values: $m\angle PTR=\frac{1}{2}(140 + 106)$.
First, calculate the sum inside the parentheses: $140+106 = 246$. Then, divide by 2: $\frac{246}{2}=123^{\circ}$.

Answer:

None of the given options are correct. The measure of $\angle PTR$ is $123^{\circ}$.