Given that the [tex]\widehat{PR}}=131^{\circ}[/tex]
We need to determine the measure of ∠PQR
Measure of ∠PQR:
The measure of ∠PQR can be determined using the formula,
[tex]m \angle PQR=\frac{1}{2}(\widehat{PSR}-\widehat{PR})[/tex]
The measure of the arc PSR can be determined by subtracting the arc PR with 360°
Thus, we have;
[tex]\widehat{PSR}=360^{\circ}-131^{\circ}=229^{\circ}[/tex]
Now, Substituting [tex]\widehat{PSR}=229^{\circ}[/tex], [tex]\widehat{PR}}=131^{\circ}[/tex] in the formula, we have;
[tex]m \angle PQR=\frac{1}{2}(229-131)[/tex]
[tex]m \angle PQR=\frac{1}{2}(98)[/tex]
[tex]m \angle PQR=49^{\circ}[/tex]
Thus, the measure of ∠PQR is 49°
