2. Construct ΔPQR if PQ = 5 cm, m∠PQR = 105o and m∠QRP = 40o.
(Hint: Recall angle-sum property of a triangle).
We know that the sum of the angles of a triangle is 180o.
∠PQR + ∠QRP + ∠RPQ = 180o
105o+ 40o+ ∠RPQ = 180o
145o + ∠RPQ = 180o
∠RPQ = 180o – 145o
∠RPQ = 35o
Hence, the measures of ∠RPQ is 35o.
Step 1. Draw a line segment PQ = 5 cm.
Step 2. Draw a ray L, at point P to make an angle of 105o i.e. ∠LPQ = 35o.
Step 3. Draw a ray M, at point Q to make an angle of 40o i.e. ∠MQP = 105o.
Step 4. Now the two rays PL and QM intersect each other at the point R.
Hence, ΔPQR is the required triangle.