Question

When the figure is rotated 180°, what will the measure of angle B equal?

Answer 1

Maritza draws a rectangle on the coordinate plane and labels the vertices A , B , C , and D . She then reflects the figure across the x -axis to get rectangle A′B′C′D′ . What is the measure of angle D′ in the reflected rectangle?(1 point)
Angle D′ measures °.

Answer 2

so what is the answer to Angle D′ measures

Answer 3

what is the answer

Answer 4

Triangle RST is drawn on the coordinate plane with vertices at (5,−6) , (5,0) , and (7,2) . The triangle is then translated 2 units to the right and 4 units down to create triangle R′S′T′ . What is the sum of the angles of triangle R′S′T′ ?
The sum of the angles is

Answer 5

When a figure is rotated 180°, all the angles are inverted or flipped. Therefore, the measure of angle B will be the same as its original measure.

Answer 6

When a figure is reflected across the x-axis, the y-coordinates of all the points are negated. Therefore, the measure of angle D' in the reflected rectangle is the same as the measure of angle D in the original rectangle.

Answer 7

I apologize for the confusion, but without any specific information about the original angle D or the shape of the rectangle, I am not able to determine the measure of angle D' in the reflected rectangle.

Answer 8

I apologize for any confusion. Without any specific information about the original angle D or the shape of the rectangle, I am unable to provide a specific answer for the measure of angle D' in the reflected rectangle.

Answer 9

To find the sum of the angles of triangle R'S'T', we need to first find the measures of each angle in the original triangle RST and then add or subtract the translation distances.

The original triangle RST has three angles: angle R, angle S, and angle T. To find the measure of angle R, we can use the distance formula to find the lengths of the two sides adjacent to angle R:

Length of RS:
√((x2 - x1)^2 + (y2 - y1)^2)
= √((5 - 5)^2 + (0 - (-6))^2)
= √(0 + 36)
= √36
= 6

Length of RT:
√((x2 - x1)^2 + (y2 - y1)^2)
= √((7 - 5)^2 + (2 - (-6))^2)
= √(4^2 + 8^2)
= √(16 + 64)
= √80
= 4√5

Now we can use the Law of Cosines to find the measure of angle R:
cos(R) = (a^2 + b^2 - c^2) / (2ab)
cos(R) = (6^2 + 4√5^2 - 4√5^2) / (2 * 6 * 4√5)
cos(R) = (36 + 80 - 80) / (48√5)
cos(R) = 36 / (48√5)
cos(R) = 3 / (4√5)

Using a calculator, we find that cos^-1(3 / (4√5)) = approximately 24.6 degrees.

Similarly, we can find the measures of angles S and T using the same process.

Afterward, we can add or subtract the translation distances to the x and y coordinates of each vertex to obtain the coordinates of R'S'T'. In this case, the triangle is translated 2 units to the right and 4 units down.

The sum of the angles in triangle R'S'T' will be the same as the sum of the angles in triangle RST, which is approximately 180 degrees.