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.