In rhombus ABCD, shown below, angle A measures 116°.

Question

If rhombus ABCD were reflected across the x-axis to create rhombus A'B'C'D', what would the measure of angle D' be?

Answer 1

When a figure is reflected across the x-axis, the y-coordinates of all the points are negated. Since a rhombus has equal opposite angles, we know that measures of angles A and C are equal, as are the measures of angles B and D. Angle A measures 116°, so angle C measures 116°. When a figure is reflected across the x-axis, angle C will occupy the same position as angle C'. In other words, angle C' has the same measure as angle C, which is 116°. Therefore, angle D' measure $\boxed{116\text{°}}$. [asy]
size(100);
pair A,B,C,D;
A=(0,0);
B=(2,2);
C=(4,0);
D=(2,-2);
draw(A--B--C--D--A);
draw(A--C);
label("A",A,SW);
label("B",B,N);
label("C",C,SE);
label("D",D,S);
[/asy]