Question

SV−→bisects ∠RST. If m∠RSV = 64, what is m∠RST?

Answer 1

Given:

$\overrightarrow{SV}$ bisects ∠RST.

$m\angle RSV=64^\circ$

To find:

The $m\angle RST$.

Solution:

Since, $\overrightarrow{SV}$ bisects ∠RST, therefore

$m\angle RSV=m\angle VST$         ...(1)

Now,

$m\angle RST=m\angle RSV+m\angle VST$

$m\angle RST=m\angle RSV+m\angle RSV$         [Using (1)]

$m\angle RST=2\times m\angle RSV$

$m\angle RST=2\times 64^\circ$              $[\text{Given }m\angle RSV=64^\circ]$

$m\angle RST=128^\circ$

Therefore, the value of $m\angle RST$ is $128^\circ$.