Question

a figure containing $\angle lmn$ is dilated by a scale factor of $\frac{1}{3}$ to form a new figure which contains $\angle lmn$. $\angle lmn$ measures $79^\circ$. what is the measure of $\angle lmn$?

Explanation:

Step1: Recall dilation property for angles

Dilation is a similarity transformation. In similar figures, corresponding angles are congruent (have the same measure).

Step2: Apply the property to the angles

Since $\angle LMN$ and $\angle L'M'N'$ are corresponding angles after dilation, their measures are equal. Given $m\angle L'M'N' = 79^\circ$, so $m\angle LMN=m\angle L'M'N'$.

Answer:

$79^\circ$