Question

Which additional fact proves that ΔRST and ΔWXY are congruent if ∠R ≅ ∠W and RS ≅ WX.

Answer 1

Answer:

C)$\angle X=2x-20$

Step-by-step explanation:

We are given that

$\angle R\cong \angle W$

$RS\cong WX$

$\angle R=2x+3$

$\angle S=x+10$

$\angle T=3x-13$

We have to find the additional fact which proves that triangle RST and triangle WXY are congruent.

In triangle RST

$\angle R+\angle S+\angle T=180^{\circ}$ (Triangle angles sum property)

Substitute the values then we get

$2x+3+x+10+3x-13=180$

$6x=180$

$x=\frac{180}{6}=30^{\circ}$

$\angle R=2(30)+3=63^{\circ}$

$\angle S=30+10=40^{\circ}$

$\angle T=3(30)-13=73^{\circ}$

$\angle R=\angle W=63^{\circ}$

When two triangles are congruent then each part of one triangle is congruent to its corresponding parts of another triangle.

Therefore, if $\triangle RST\cong \triangle WXY$

Then, $\angle S\cong \angle X, \angle T\cong \angle Y$

Therefore, $\angle Y=73^{\circ}$

$\angle X=40^{\circ}$

$\angle X=2(30)-20=40^{\circ}$

Hence, option C is correct.

Answer 2

Answer:c

Step-by-step explanation: