Question

select the correct answer.
a similarity transformation maps ( \triangle abc ) to ( \triangle jkl ). the measure of ( angle a ) of preimage ( \triangle abc ) is ( 105^circ ). the scale factor of the dilation in the similarity transformation is 1.5. if ( angle a ) in the preimage corresponds to ( angle j ) in the image, what is ( mangle j )?

a. ( 70^circ )
b. ( 140^circ )
c. ( 105^circ )
d. ( 35^circ )

Explanation:

Step1: Recall properties of similarity transformations

In a similarity transformation, corresponding angles of similar figures are congruent (they have the same measure). This is a key property of similar triangles (or any similar polygons).

Step2: Apply the property to the given angles

Since \( \triangle ABC \) is mapped to \( \triangle JKL \) by a similarity transformation, and \( \angle A \) corresponds to \( \angle J \), the measure of \( \angle J \) should be equal to the measure of \( \angle A \).
We know that \( m\angle A = 105^\circ \), so by the property of similar figures, \( m\angle J = m\angle A = 105^\circ \).

Answer:

C. \( 105^\circ \)