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– 1450
= ∠RPQ = 35o
Hence, the measures of ∠RPQ is 35o.
The steps for construction are given below:
1. Draw a line segment PQ = 5 cm.
2. At point P, draw a ray L to making an angle of 105o i.e. ∠LPQ = 35o.
3. At point Q, draw a ray M to making an angle of 40o i.e. ∠MQP = 105o.
4. Now the two rays PL and QM intersect at the point R.
Then, ΔPQR obtained is the required triangle.