Answer:
A
Step-by-step explanation:
We know that ∠[tex]ABE[/tex] ≅ ∠[tex]DBC[/tex] because they are vertical angles, so that's one pair of congruent angles. However, we can't compare ∠[tex]BAE[/tex] and ∠[tex]DCB[/tex] as they have different measures, so we'll have to find the measure of either ∠[tex]AEB[/tex] or ∠[tex]BDC[/tex]. Let's go with the former. Using the fact that the sum of the measures of the interior angles of a triangle is [tex]180[/tex]°, we know that [tex]m[/tex]∠[tex]AEB=180-(53+42)=180-95=85[/tex]°. Now, we know that ∠[tex]AEB[/tex] ≅ ∠[tex]DCB[/tex] because their measures are equal. That's another pair of congruent angles. Therefore, the angles are similar by [tex]AA[/tex]. Hope this helps!
