Question

in the diagram below, (mwidehat{ps}=60^{circ}) and (mwidehat{qr}=74^{circ}). what is the measure of (angle pts)?

Explanation:

Step1: Recall the formula for the measure of an angle formed by two chords.

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

Step2: Substitute the given arc - measures into the formula.

We are given that $m\overparen{PS} = 60^{\circ}$ and $m\overparen{QR}=74^{\circ}$. So, $\angle PTS=\frac{1}{2}(60 + 74)$.

Step3: Calculate the value.

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

Answer:

B. $67^{\circ}$