question_answer 12)

Construct \[\Delta PQR\] if \[PQ=5cm,\] \[m\angle PQR={{105}^{\text{o}}}\]and \[m\angle QRP={{40}^{\text{o}}}\](Hint: Recall angle-sum property of a triangle).              

Answer:

                Steps of construction 1. Draw PQ of length 5 cm. 2. At Q, draw a ray QX making an angle. 3. At P draw a ray PY making an angle of \[\text{3}{{\text{5}}^{\text{o}}}\] with PQ By angle-sum property of a triangle \[m\angle RPQ+m\angle PQR+m\angle QRP={{180}^{\text{o}}}\] \[\Rightarrow \]               \[m\angle RPQ+{{105}^{\text{o}}}+{{40}^{\text{o}}}={{180}^{\text{o}}}\] \[\Rightarrow \]               \[m\angle RPQ+{{145}^{\text{o}}}={{180}^{\text{o}}}\] \[\Rightarrow \]               \[m\angle RPQ={{35}^{\text{o}}}\] 4. Mark the point of intersection of two rays as R. \[\Delta \Rho QR\]is now completed.