In triangle DEF, m<D=51°, m<E=68°, and m<F=61°. Triangle DEF is translated 10 units to the left and 2 units down to create triangle D'E'F'. If x represents the measure of angle D' and y represents the measure of angle D', what is the value of x + y?
Since triangle DEF is translated 10 units to the left and 2 units down to create triangle D'E'F', the corresponding angles will have the same measures. Therefore, m<D' = 51°, m<E' = 68°, and m<F' = 61°.
Since the sum of the angles in a triangle is 180°, we have:
m<D' + m<E' + m<F' = 180°
51° + 68° + 61° = 180°
180° = 180°
Therefore, x + y = 180°.
To find the value of x + y, we need to determine the measures of angles D' and E' in triangle D'E'F'.
Since triangle DEF is translated 10 units to the left and 2 units down to create triangle D'E'F', the angles in triangle D'E'F' are congruent to the corresponding angles in triangle DEF.
Given that m<D = 51°, the measure of angle D' in triangle D'E'F' is also 51°.
Similarly, m<E = 68°, so the measure of angle E' in triangle D'E'F' is also 68°.
Therefore, x = 51° and y = 68°.
To find the value of x + y, we simply add the measures of angles D' and E':
x + y = 51° + 68° = 119°.
Thus, the value of x + y is 119°.
To find the value of x + y, we need to determine the measures of angles D' and E' in triangle D'E'F'.
First, let's analyze the translation. The triangle is translated 10 units to the left and 2 units down. This means that every point in the triangle is shifted 10 units to the left and 2 units down.
To find the location of point D' after the translation, we subtract 10 from the x-coordinate of point D and subtract 2 from the y-coordinate of point D. Similarly, we can find the location of point E' by subtracting 10 from the x-coordinate of point E and subtracting 2 from the y-coordinate of point E.
Now, let's calculate the coordinates of points D' and E'.
Given that point D has coordinates (xD, yD), after the translation, the coordinates of D' become (xD - 10, yD - 2).
Given that point E has coordinates (xE, yE), after the translation, the coordinates of E' become (xE - 10, yE - 2).
Now that we know the coordinates of points D' and E', we can proceed with finding their angle measures.
Angle D' is the same as angle D, so m<D' = m<D = 51°.
Angle E' is the same as angle E, so m<E' = m<E = 68°.
Therefore, the value of x (angle D') is 51°, and the value of y (angle E') is 68°.
To find the value of x + y, we simply add the measures of angles D' and E':
x + y = 51° + 68° = 119°.
So, the value of x + y is 119°.