Answer:
Option C.
Step-by-step explanation:
In the given figure C is the center of the circle.
Let A and B are two points on the circle, such that
[tex]\angle A=a^{\circ},\angle B=b^{\circ}[/tex]
Since CA and CB are radius of the circle, therefore ABC is an isosceles triangle.
[tex]\angle A=\angle B=a^{\circ}[/tex]
Using angle sum property,
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]a^{\circ}+a^{\circ}+\angle C=180^{\circ}[/tex]
[tex]2a^{\circ}=180^{\circ}-\angle C[/tex]
Divide both sides by 2.
[tex]a^{\circ}=\dfrac{180^{\circ}-\angle C}{2}[/tex]
It is given that
[tex]30<C<60[/tex]
[tex]\Rightarrow 180-30>180-C>180-60[/tex] (Subtract from 180)
[tex]\Rightarrow 150>180-C>120[/tex]
[tex]\Rightarrow \dfrac{150}{2}>\dfrac{180-C}{2}>\dfrac{120}{2}[/tex] (Divide by 2)
[tex]\Rightarrow 75>a>60[/tex]
[tex]\Rightarrow 60<a<75[/tex]
Hence, the correct option is C.
