Answer: It does not confirm that ΔABC∼ΔA'B'C by the AA criterion as the measure of angle B is negative which is not possible.
Step-by-step explanation:
Since we have given that
In ΔABC,
∠A = 8x - 10, ∠B = 10x - 40, and ∠C = 3x + 20
In ΔA'B'C',
∠A' = 6x + 10, ∠B' = 70 - x, and ∠C' = 10x 2
Since ΔABC gets a dilation by a scale factor of [tex]\dfrac{1}{2}[/tex]
So, it becomes,
[tex]\dfrac{\angle A}{\angle A'}=\dfrac{1}{2}\\\\\dfrac{8x-10}{6x+10}=\dfrac{1}{2}\\\\2(8x-10)=6x+10\\\\16x-20=6x+10\\\\16x-6x=10+20\\\\10x=30\\\\x=\dfrac{30}{10}=3[/tex]
Now, put the value of
[tex]\angle B=10(3)-40=30-40=-10\\\\and \angle B'=70-30=40[/tex]
It does not confirm that ΔABC∼ΔA'B'C by the AA criterion as the measure of angle B is negative which is not possible.
