Question

What is the answer to this problem

Answer 1

When two pentagons are congruent, then the corresponding angles and sides are equal (congruent).

As, Pentagon $GDXLP\cong$ Pentagon $ARKMV$

Being congruent, the corresponding sides are equal(congruent).

So, $\overline{GD} \cong \overline{AR}$ , $\overline{DX} \cong \overline{RK}$ , $\overline{XL} \cong \overline{KM}$ , $\overline{LP} \cong \overline{MV}$ , $\overline{GP} \cong \overline{AV}$ , $\overline{GL} \cong \overline{AM}$ , $\overline{DL} \cong \overline{RM}$ , $\overline{DP} \cong \overline{RV}$ and $\overline{XP} \cong \overline{KV}$

Being Congruent, corresponding angles are also equal (congruent).

So, $\angle G \cong \angle A$ , $\angle D \cong \angle R$ , $\angle X \cong \angle K$ , $\angle L \cong \angle M$ , $\angle P \cong \angle V$

Therefore, Option 2 , 4 and 5 are correct.

That is,$\angle X \cong \angle K$

$\overline{GP} \cong \overline{AV}$

and $\overline{PL} \cong \overline{VM}$