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Important questions based on NCERT syllabus for Class 7 Chapter 3 - Understanding Quadrilaterals:
Question 1: Given 2 unequal sides and one angle of a parallelogram, how many such parallelograms are possible?
For a parallelogram with 2 unequal sides known, all 4 sides are known because 2 pairs of opposite sides are equal.
If one angle is known, all the other 4 angles are known because adjacent angles are supplementary and opposite are equal.
Hence, all angles and all sides are known. Hence there is only one parallelogram that can be created with given data.
Question 2: If each interior angle of a regular polygon is 150o, how many sides does this polygon have?
Solution: Each interior angle of the polygon
Each exterior angle of the polygon
∴ Number of sides of this polygon
360/30 = 12
Hence, Number of sides = 12
Question 3: Ankush prepared a poster in the form of a parallelogram, as in figure.
(i) If ∠A = (5x + 7)o and ∠B = (3x − 3)o, find all the angles of paralllelogram ABCD.
(ii) Which mathematical concept is used in this question?
(iii) By writing a slogan on the poster, which value is depicted by Ankush?
(i) Since sum of adjacent angles of a parallelogram is 180∘
∴ We have ∠A + ∠B = 180o
⇒ 5x + 7 +3x − 3 = 180o
⇒ 8x + 4 = 180o
⇒ 8x = 176o
⇒ x = 176/8 = 22o
∴ ∠A = (5x+7)o = (5×22+7)o = 117o
∠B = (3x−3)o = (3×22−3)o = 63o
∠C = ∠A = 117o (opposite angles of parallelogram)
∠D = ∠A = 63o
(ii) Properties of parallelogram
(iii) Energy conservation is very necessary for a happy and prosperous future.