<PRE><B>Question 1190326</B>
&lt;br&gt;
Let 2x be the measure of the angle that is bisected; so the measures of angles PQS and RQS are each x.  Then&lt;br&gt;
Using the law of cosines on triangle QRS,&lt;br&gt;
{{{45^2=50^2+30^2-2(50)(30)cos(x)}}} [1]&lt;br&gt;
Using the law of cosines on triangle PQS,&lt;br&gt;
{{{x^2=18^2+30^2-2(18)(30)cos(x)}}} [2]&lt;br&gt;
Solve [1] for cos(x) and substitute in [2].&lt;br&gt;
I&#39;ll leave it to you to do the calculations....&lt;br&gt;
If you only want the answer, without a chance to learn something from working on the problem, the answer is PS=27.&lt;br&gt;
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