Given:
The radius of the circle = 12 in.
The central angle of the intercepted arc PQ = 135 degrees.
To find:
The measure of arc PQ.
Solution:
The length of arc is:
[tex]s=2\pi r\times \dfrac{\theta}{360^\circ}[/tex]
Where, r is the radius and [tex]\theta [/tex] is the central angle.
Substituting [tex]r=12,\pi=3.14,\theta=135^\circ[/tex] in the above formula, we get
[tex]s=2(3.14)(12)\times \dfrac{135^\circ}{360^\circ}[/tex]
[tex]s=75.36\times 0.375[/tex]
[tex]s=28.26[/tex]
[tex]s\approx 28.3[/tex]
The measure of arc PQ is 28.3 in. Therefore, the correct option is (d).