Question 1. In the adjoining figure, ABCD is a trapezium in which AB || DC. If ∠A = 35º and ∠B = 75º, then find ∠C and ∠D.
Solution: AB || DC and AD is a transversal.
∴ ∠A + ∠D = 180º
⇒ ∠D = 180° - ∠A
= 180° - 35° = 145°
Similarly, ∠B + ∠C = 180º
⇒ ∠C = 180° - 75° = 105°
Thus, ∠C = 105°∠D = 145°
Question 2. Fill in the blanks:
(i) In a parallelogram, opposite angles are ____.(ii) A ____ of a parallelogram divides it into two congruent triangles. (iii) The sum of the angles of a quadrilateral is ____. (iv ) In a parallelogram, the opposite sides are parallel and _____.
Solution: (i) equal
Question 3. One angle of a quadrilateral is 140° and other three angles are in the ratio of 3 : 3 : 2.
Find the measure of the smallest angle of the quadrilateral.
Solution: Remaining three angles = 360° - 140° = 220°
Ratio is 3 : 3 : 2
∴ The smallest angle