Which additional fact proves that ΔRST and ΔWXY are congruent if ∠R ≅ ∠W and RS ≅ WX.∠R = 2x + 3 ∠S = x + 10∠T = 3x - 13A) ∠X = x + 33 B) ∠Y = x + 33 C) ∠X = 2x - 20 D) ∠Y = 2x - 20

Answer:C)[tex]\angle X=2x-20[/tex]Step-by-step explanation:We are given that [tex]\angle R\cong \angle W[/tex][tex]RS\cong WX[/tex][tex]\angle R=2x+3[/tex][tex]\angle S=x+10[/tex][tex]\angle T=3x-13[/tex]We have to find the additional fact which proves that triangle RST and triangle WXY are congruent.In triangle RST[tex]\angle R+\angle S+\angle T=180^{\circ}[/tex] (Triangle angles sum property)Substitute the values then we get [tex]2x+3+x+10+3x-13=180[/tex][tex]6x=180[/tex][tex]x=\frac{180}{6}=30^{\circ}[/tex][tex]\angle R=2(30)+3=63^{\circ}[/tex][tex]\angle S=30+10=40^{\circ}[/tex][tex]\angle T=3(30)-13=73^{\circ}[/tex][tex]\angle R=\angle W=63^{\circ}[/tex]When two triangles are congruent then each part of one triangle is congruent to its corresponding parts of another triangle.Therefore, if [tex]\triangle RST\cong \triangle WXY[/tex]Then, [tex]\angle S\cong \angle X, \angle T\cong \angle Y[/tex]Therefore, [tex]\angle Y=73^{\circ}[/tex][tex]\angle X=40^{\circ}[/tex][tex]\angle X=2(30)-20=40^{\circ}[/tex]Hence, option C is correct.