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For the triangles shown, triangle ABC is dilated by a scale factor of 5 to obtain triangle XYZ, where \( d=17 \). What is the measure, in degrees, of angle X?

Triangle \( ABC \) is similar to triangle \( XYZ \), where \( A \), \( B \), and \( C \) correspond to \( X \), \( Y \), and \( Z \), respectively. In triangle \( ABC \), the length of \( AB \)  is 120 and the length of \( BC \)  is 600. In triangle \( XYZ \), the length of \( YZ \)  is 80. What is the length of \( XY \) ?

Triangle \( ABC \) is similar to triangle \( XYZ \), where \( A \), \( B \), and \( C \) correspond to \( X \), \( Y \), and \( Z \), respectively. In triangle \( ABC \), the length of \( AB \)  is 130 and the length of \( BC \) is 650. In triangle \( XYZ \), the length of \( YZ \) is 70. What is the length of \( XY \)?

Triangle TUV is dilated by a scale factor of \( \frac{1}{2} \)to obtain triangle T'U'V'  (not shown), where T  corresponds to T'  and U corresponds to U' . What is the measure, in degrees, of angle V'?

Triangles ABC and DEF are similar. Each side length of triangle ABC is 4 times the corresponding side length of triangle DEF. The area of triangle ABC is 270 square inches. What is the area, in square inches, of triangle DEF?

Triangle \( ABC \) is similar to triangle \( XYZ \), where \( A \), \( B \), and \( C \) correspond to \( X \), \( Y \), and \( Z \), respectively. In triangle \( ABC \), the length of \( AB \) is 170 and the length of \( BC \) is 850. In triangle \( XYZ \), the length of \( YZ \) is 60. What is the length of \( XY \) ?

Triangles \( ABC \) and \( DEF \) are congruent, where \( A \) corresponds to \( D \), and \( B \) and \( E \) are right angles. The measure of angle \( A \) is 18°. What is the measure of angle \( F \)?

Triangles \( ABC \) and \( DEF \) are congruent, where \( A \) corresponds to \( D \), and \( B \) and \( E \) are right angles. The measure of angle \( A \) is 18°. What is the measure of angle \( F \)?

Triangles \( ABC \) and \( DEF \) are congruent, with \( A \) corresponding to \( D \), and \( B \) and \( E \) being right angles. The measure of \( A \) is \( 27^{∘} \). We need to find the measure of \( F \).

In the figure shown, \( WZ \) and \( XY \)  intersect at point \( Q \), \( YQ=21 \) , \( WQ=70 \), \( WX=60 \) , and \( XQ=120 \). What is the length of \( YZ \)?

In the figure shown, \( WZ \) and \( XY \)  intersect at point \( Q \), \( YQ=21 \) , \( WQ=70 \), \( WX=60 \), and \( XQ=120 \). What is the length of \( YZ \)?

In triangles LMN and RST, angles L and R each have measure 60°，LN = 10, and RT=30.Which additional piece of information is sufficient to prove that triangle LMN is similar to triangle RST?