Select the correct answer. which transformation will always map a parallelogram onto itself? a. a 90° rotation about its center b. a reflection across one of its diagonals c. a 180° rotation about its center d. a reflection across a line joining the midpoints of opposite sides

C. a 180° rotation about its center

Step-by-step explanation:

The question is on rotation of an object about the origin through 180°

When a point B, (h,k) is rotated about the origin 0 through 180° both clockwise and anticlockwise directions , the new position is B'(-h,-k)

Example, if we have point K (5,8) rotated through 180°, clockwise or anti-clockwise about the origin the new position will be; K'(-5,-8)

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq