Question

The hexagon GIKMPR is regular. The dashed line segments form 30 degree angles.

What is the angle of rotation about 0 that maps PQ to RF?
A) 240°
B) 210°
C) 90°
D) 300°

Answer 1

Answer:

The correct option is (D).

Step-by-step explanation:

It is given that GIKMPR is regular hexagon. It means it has 6 vertices.

Since the central angle is 360 degree. Therefore the central angle between two consecutive vertices is

$\frac{360^{\circ} }{6}=60^{\circ}$

It is given that the dashed line segments form 30 degree angles.

We have rotated the hexagon about O to map PQ to RF. Since P and R are consecutive vertices, therefore the angle between them is 60 degree.

The vertex R is immediate next to the vertex P in clockwise direction.

So if we rotate the hexagon at 60 degree clockwise about O, then we can maps PQ to RF.

$360^{\circ}-60^{\circ}=300^{\circ}$

Therefore we can also rotate the hexagon at 300 degree counterclockwise about O, then we can maps PQ to RF.

Therefore option D is correct.