In the given figure, AP is perpendicular to BC, and AQ is the bisector of angle PAC. What will be the measure of angle PAQ ?

From the given figure,

AP is perpendicular to BC

$$=$$>  $$\angle\ $$APC = $$90^{\circ}$$

In $$\triangle\ $$PAC,

$$\angle\ $$PAC + $$\angle\ $$APC + $$\angle\ $$PCA = $$180^{\circ\ }\ $$

$$=$$> $$\angle\ $$PAC +  $$90^{\circ}$$ + $$30^{\circ}$$ = $$180^{\circ\ }$$

$$=$$> $$\angle\ $$PAC = $$180^{\circ}-120^{\circ}$$

$$=$$> $$\angle\ $$PAC = $$60^{\circ}$$

AQ is the bisector of angle PAC

$$=$$> $$\angle\ $$PAQ = $$\frac{60^{\circ\ }}{2}$$

$$=$$> $$\angle\ $$PAQ = $$30^{\circ\ }$$

Hence, the correct answer is Option D