Question

question 12 of 25
in the diagram below, ( moverarc{pr} = 140^circ ) and ( moverarc{qs} = 106^circ ). what is the measure of ( angle ptr )?

a. ( 123^circ )
b. ( 246^circ )
c. ( 106^circ )
d. ( 140^circ )

Explanation:

Step1: Recall intersecting chords angle theorem

The measure of an angle formed by two intersecting chords inside a circle is half the sum of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The intercepted arcs for $\angle PTR$ are $\overset{\frown}{PR}$ and $\overset{\frown}{QS}$, with measures $140^\circ$ and $106^\circ$.

Step3: Calculate the angle measure

$$m\angle PTR = \frac{1}{2} \times (m\overset{\frown}{PR} + m\overset{\frown}{QS}) = \frac{1}{2} \times (140^\circ + 106^\circ)$$
$$= \frac{1}{2} \times 246^\circ = 123^\circ$$

Answer:

A. $123^\circ$