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 the property of similar triangles

Similar triangles have congruent corresponding angles. A similarity transformation (which includes dilation) preserves the measure of angles.

Step2: Apply the property to the given angles

Since \(\triangle ABC\) and \(\triangle JKL\) are similar (due to the similarity transformation) and \(\angle A\) corresponds to \(\angle J\), \(m\angle A=m\angle J\). Given \(m\angle A = 105^{\circ}\), so \(m\angle J=105^{\circ}\).

Answer:

C. \(105^{\circ}\)