NCERT Solutions For Class 7 Maths Chapter 10 Practical Geometry Exercise 10.4

Q.2. Construct ∆PQR if PQ = 5 cm, m∠PQR = 105° and m∠QRP = 40°. (Hint: Recall angle-sum property of a triangle).

Ans:

We know that the sum of the angles of a triangle is 180^o.

∴          m∠PQR + m∠QRP + m∠RPQ = 180^o

⟹        105^o+ 40^o+ ∠RPQ = 180^o

⟹        145^o + ∠RPQ = 180^o

⟹        ∠RPQ = 180^o– 145⁰

⟹        ∠RPQ = 35^o

Steps of construction:

1. Draw a line segment PQ = 5 cm.
2. At point P, draw an angle of 35^oi.e. ∠XPQ = 35^o.
3. At point Q, draw an angle of 105^oi.e. ∠YQP = 105^o.
4. Now PX and QY intersect at the point R.

Then, ΔPQR is the required triangle.