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.
Therefore, ∠A + ∠D = 180° (co-interior angles on the same side of the transversal).
∴ ∠D = 180° – ∠A = 180° – 35° = 145°.
Similarly, since AB || DC and BC is a transversal, ∠B + ∠C = 180° (co-interior angles).
∴ ∠C = 180° – ∠B = 180° – 75° = 105°.
Thus, ∠C = 105° and ∠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: Ans: (i) equal
(ii) diagonal
(iii) 360°
(iv) 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 of the three angles = 3 : 3 : 2.
Sum of ratio parts = 3 + 3 + 2 = 8.
∴ One part = 220° ÷ 8 = 27.5°.
∴ The smallest angle = 2 × 27.5° =
= 55°.
Hence, the smallest angle of the quadrilateral is 55°.