For ΔABC, ∠A = 3x - 8, ∠B = 5x - 6, and ∠C = 4x + 2. If ΔABC undergoes a dilation by a scale factor of 1 2 to create ΔA'B'C' with ∠A' = 2x + 8, ∠B' = 90 - x, and ∠C' = 5x - 14, which confirms that ΔABC∼ΔA'B'C by the AA criterion? A) ∠A = ∠A' = 37° and ∠B = ∠B' = 69° B) ∠A = ∠A' = 22° and ∠C = ∠C' = 42° C) ∠B = ∠B' = 37° and ∠C = ∠C' = 33° D) ∠B = ∠B' = 74° and ∠C = ∠C' = 66°

Answer:D. ∠B = ∠B' = 74° and ∠C = ∠C' = 66°Step-by-step explanation:Given, [tex]\angle A=3x-8\\\angle B=5x-6\\\angle C=4x+2[/tex]We know,sum of all 3 angles of a triangle is [tex]180[/tex]°Doing so , [tex]\angle A+\angle B+\angle C=180\\3x-8+5x-6+4x+2=180[/tex]Simplifying all like terms,[tex]12x-12=180\\12x-12+12=180+12\\12x=192[/tex]Dividing both side by 12[tex]x=\frac{192}{12}[/tex][tex]x=16[/tex]Now we plug this in each angles and find their exact values.[tex]\angle A=3x-8=(3\times16)-8=48-8=40[/tex]°[tex]\angle B=5x-6=(5\times16)-6=80-6 =74[/tex]°[tex]\angle C=4x+2 = (4\times16)+2=64+2=66[/tex]°Now substituting the [tex]x=16[/tex] in angles of dilated triangle.[tex]\angle A'=(2\times16)+8=32+8= 40[/tex]°[tex]\angle B'=90-16=74 [/tex]°[tex]\angle C'=(5\times16)-14=80-14=66[/tex]°We see that all the corresponding angles are equal and as far as the options are concerned only option (D) matches.