91Ó°ÊÓ

$\stackrel{→}{SV}$ bisects$∠RST$ and$\stackrel{→}{RU}$ bisects $∠SRT$ .

An angle bisector bisects the angle into two congruent angles.

As $\stackrel{→}{SV}$bisects $∠RST$,

$∠TSVâ‰\dots ∠RSV$

As $\stackrel{→}{RU}$bisects $∠SRT$,

$∠SRUâ‰\dots ∠TRU$.

Therefore, the congruent angles are $∠TSV,∠RSV$and $∠SRU,∠TRU$.

$\stackrel{→}{SV}$ bisects$∠RST$ and$\stackrel{→}{RU}$ bisects $∠SRT$ .

The congruent angles are $∠TSV,∠RSV$and$∠SRU,∠TRU$ as obtained in part (a).

Given:$m∠VSR=m∠URV$

If two angles are congruent then their measures are also equal.

From part (a), $∠TSVâ‰\dots ∠RSV$, so,

$m∠TSV=m∠RSV$ …… (1)

From part (a), $∠SRUâ‰\dots ∠TRU$, so,

$m∠SRU=m∠TRU$ …… (2)

Now assume $m∠VSR=m∠URS$ …… (3)

From (1), (2) and (3),

$m∠TSV=m∠TRU$.

That is,

$m∠VSU=m∠URV$

Therefore, the additional information required to deduce $m∠VSU=m∠URV$is $m∠VSR=m∠URS$.