Rectangle lmnp is rotated, using the origin as the center of rotation, to form rectangle l’m’n’p’. what is the angle of rotation?

The answer is 180°.

Step-by-step explanation: As given in the figure, using the origin as centre of rotation, rectangle LMNP is rotated to form the rectangle L'M'N'P'. We need to find the angle of rotation here.

The co-ordinate of the vertices of rectangle LMNP are L(-2,5), M(1,5), N(1,4) and P(-2,4) and the vertices of rectangle L'M'N'P' after rotation are L'(2,-5), M'(-1,-5), N'(-1,-4) and P'(2,-4).

Therefore, if the co-ordinates of the vertices of rectangle LMNP be represented by (x,y), then the co-ordinate of the vertices of rectangle L'M'N'P' will be (-x,-y).

That is, there will be a jump of two consecutive quadrants. Hence, the angle of rotation will be 2 × 90° = 180°.

Thus, the answer is 180°.