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Sagot :
Given the figure in the attached image;
[tex]\begin{gathered} m\measuredangle\text{PRQ}=25^{\circ} \\ m\measuredangle QTU=105^{\circ} \end{gathered}[/tex]The angle PQS and QTU are corresponding angles so they are congruent.
[tex]m\measuredangle PQS=m\measuredangle QTU=105^{\circ}[/tex]Also, the angle PQS is an exterior angle to the angles PRQ and RPQ. So, the sum of angles PRQ and RPQ will give the angle PQS;
[tex]m\measuredangle PQS=m\measuredangle PRQ+m\measuredangle RPQ[/tex]substituting the given values;
[tex]\begin{gathered} m\measuredangle PQS=m\measuredangle PRQ+m\measuredangle RPQ \\ 105^{\circ}=25^{\circ}+m\measuredangle RPQ \\ m\measuredangle RPQ=105^{\circ}-25^{\circ} \\ m\measuredangle RPQ=80^{\circ} \end{gathered}[/tex]Therefore, the measure of angle RPQ is;
[tex]m\measuredangle RPQ=80^{\circ}[/tex]
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