Question

question 6 of 25 in the diagram below, m\\(\widehat{ps}\\) = 60° and m\\(\widehat{qr}\\) = 74°. what is the measure of \\(\angle pts\\)?

Explanation:

Step1: Recall the formula

The measure of an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs. So, $m\angle PTS=\frac{1}{2}(m\overparen{PS} + m\overparen{QR})$.

Step2: Substitute the given values

We know that $m\overparen{PS}=60^{\circ}$ and $m\overparen{QR}=74^{\circ}$. Substituting these values into the formula, we get $m\angle PTS=\frac{1}{2}(60 + 74)$.

Step3: Calculate the result

First, add the values inside the parentheses: $60+74 = 134$. Then, divide by 2: $\frac{134}{2}=67^{\circ}$.

Answer:

C. 67°