# Practical Geometry

## Exercise 10.4

**Question 1:** Construct ΔABC, given m∠A = 60°, m∠B = 30° and AB = 5.8 cm.

**Answer:** Draw a line AB = 5.8 cm.

Make an angle of 60° on point A and another angle of 30° on point B.

The lines from A and B intersect at point C.

This gives the required triangle.

**Question 2:** Construct ΔPQR if PQ = 5 cm, m∠PQR = 105° and m∠QRP = 40°.

**Answer:** Draw a line PQ = 5 cm.

With the help of a protractor, make an angle of 105° at point Q.

Since 180 – (105 + 40) = 35, hence make an angle of 35° at point P.

Draw lines from points P and Q as per the angles; so that the lines intersect at point R.

**Question 3:** Examine whether you can construct DDEF such that EF = 7.2 cm, m∠E = 110° and m∠F = 80°. Justify your answer.

**Answer:** The sum of two angles in this question is more than 180°. We know that sum of all angles of a triangle is 180°. Hence, this triangle is not possible.

This question is based on angle sump property of triangle, which says that sum of all angles of a triangle is equal to two right angles.