The measure of the [tex]\angle PQS[/tex] = [tex]70^{o}[/tex]
We have an angle [tex]\angle PQR = 140^{o}[/tex] and QS is the angle bisector [tex]\angle PQR[/tex].
We have to find the value of [tex]\angle PQS[/tex].
The term bisecting the angle means dividing the angle (say [tex]x^{o}[/tex]) into two equal angles. The measure of each angle formed will be equal to [tex]\frac{x^{o} }{2}[/tex].
In the question given to us -
[tex]\angle PQR = 140^{o}[/tex] and QS is the angle bisector.
Now, QS will bisect the angle PQR into two equal parts such that the measure of each part will be = [tex]\frac{\angle PQR}{2}[/tex] = [tex]\frac{140^{o} }{2} = 70^{o}[/tex].
Hence, the measure of the [tex]\angle PQS[/tex] = [tex]70^{o}[/tex]
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