Construct ΔPQR if PQ = 5 cm, m∠PQR = 105o and m∠QRP = 40o. (Hint: Recall angle-sum property of a triangle).

Solution

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.

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