Answer:
The measure of angle Q'R'S' is 35°
Explanation:
The given parameters are;
The measure of angle QRS = 35°
The transformation applied to triangle QRS = 90° clockwise rotation
For a 90° clockwise rotation, we have;
Coordinate of the preimage (x, y), coordinate of the image after rotation (y, -x)
Given that the distance, d, between points is given by √((x₂ - x₁)² + (y₂ - y₁)²), we have that the distance between points of the image will be given as follows;
d' =√((y₂ - y₁)² + ((-x₂) - (-x₁))²) = √((y₂ - y₁)² + (x₁ - x₂)²)
Whereby we have √((y₂ - y₁)² + (x₁ - x₂)²) = √((x₂ - x₁)² + (y₂ - y₁)²)
Therefore, d = d' and the length of the sides and measures of the angles in ∠QRS and ∠Q'R'S' will be equal and ∠Q'R'S' = ∠QRS = 35°.