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.
