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Practical Geometry topic in Class 8th Mathematics deals with the study basic shapes and their construction. The chapter discusses the theory, rules and steps to construct the polygons and shapes.
Chapter-4 Practical Geometry carries 8 Marks in total according to the Class-8 Mathematics marking scheme. The article discusses few Multiple-Choice Questions (MCQs) related to the Class-8 Mathematics, Chapter-4: Practical Geometry.
Read: NCERT Solutions for Class 8 Mathematics Chapter 4: Practical Geometry
Ques. What is needed to know before constructing a square?
a) All the interior angles
b) All the side lengths
c) Only one interior angle
d) Only one side length
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Ans. (d)
Explanation: All the sides of a square are equal to each other and the interior angles of a square is perpendicular to each other that is equal to 90o. So, if we know the length of any one side of a square, then we can construct a square effectively.
Ques. How to construct a parallelogram and a rectangle?
a) If we know the length of its parallel sides and all the interior angles
b) Measure of interior angles and all the sides
c) Two adjacent sides and one angle, only length and breadth
d) Two adjacent sides and two angles, measures of any one angle
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Ans. (c)
Explanation: All the parallel sides of a parallelogram are equal to each other. To construct a parallelogram, we must need to know about any one angle, then we can obtain the other angle as the two angles are supplementary angles. And for constructing a rectangle, if the length and breadth of a rectangle are known, then we can construct it easily. The sides of a rectangle have parallel sides with each angle is equal to 90o.
Ques. What is the total sum of all the interior angles of a parallelogram?
(a)180°
(b) 360°
(c) 540°
(d) 240°
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Ans. (b)
Explanation: The sides of a parallelogram are equal and parallel to each other. All the interior angles of a parallelogram are perpendicular and the value of each angle is equal to 90o. So, if we add all the interior angles of a parallelogram, it is equal to 360o.
Ques. What is the value of x, if the interior angles of a quadrilateral are 130°, 120°, 50 °, and x°?
(a) 120°
(b) 80°
(c) 100°
(d) 60°
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Ans. (d)
Explanation: As per the interior angle sum property of a quadrilateral sum of all interior angles is equal to 360o. Hence,
120° + 130° + 50° + x° = 360°
300° + x° = 360°
x° = 360° - 300°
x° = 60°
Ques. What is the name of a polygon if it has minimum number of sides?
(a) Triangle
(b) Square
(c) Rectangle
(d) Angle
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Ans. (a)
Explanation: As we know that angles are not a polygon, as it does not have a closed shape. However, the arms of an angle extended indefinitely. The triangle is a type of polygon having all its sides equal.
Ques. What is the number of diagonals in a polygon, if the number of its sides is equal to n?
(a) n/2
(b) n/3
(c) n(n-3)/2
(d) n(n-3)/3
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Ans. (c): n(n-3)/2
Explanation: In a quadrilateral, the number of sides is equal to 4.
n (n-3) / 2 = 4 (4-3) / 2 = 4 / 2 = 2
Hence, the quadrilateral has two diagonals.
Ques. Calculate the sum of all the interior angles of a hexagon?
(a) 720°
(b) 540°
(c) 360°
(d) 180°
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Ans. (a) 720°
Explanation: As we know that the total number of sides of a hexagon is equal to 6, so we take n = 6.
The formula of all the sum of interior angles = (n-2) x 180°
Now out the value of n in the formula we get
= (6 – 2) x 180°
= 720°
Hence, the sum of interior angles of a hexagon is 720°.
Ques. If the sum of all the interior angles of a regular polygon is equal to 540° then what is the name of that polygon?
(a) Quadrilateral
(b) Pentagon
(c) Hexagon
(d) Septagon
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Ans. (b) Pentagon
Explanation: The total sum of interior angles is given in the question so if we know about the number of sides then the name of a polygon can be determined.
Now, according to the question
The formula of sum of interior angles =
(n-2) x 180°
Now, as we know that the sum is 540°, putting the value we get
540° = (n – 2) x 180°
n – 2 = 540° / 180°
n -2 = 3
n = 3 + 2
n = 5.
Thus, the name of a polygon is pentagon as the number of sides is equal to 5.
Ques. All the sides of a regular polygon are ___? Sum of all the exterior angles of a polygon is?
(a) Equal in length, 360°
(b) Unequal in length, 180°
(c) Parallel to each other, 540°
(d) None of these, 720°
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Ans. (a) Equal in length, 360°
Explanation: The sides of a regular polygon are equal in length as well as all its angles are equal in measures. And the sum of all exterior angles of a polygon is equal to 3600.
Ques. Is it possible to draw a square with a side length equal to the value of 7cm?
(a) Yes
(b) No
(c) Cannot be determined
(d) None of the above
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Ans. (a) Yes
Explanation: As we know that all the sides of a square are equal in length and the value of all the interior angles is equal to 90 degrees. Hence, we can use any of the five measurements to construct a square.
Ques. If the sum of all the interior angles of a regular polygon is equal to 720° then what is the name of that polygon?
(a) Quadrilateral
(b) Pentagon
(c) Hexagon
(d) Septagon
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Ans. (c) Hexagon
Explanation: The total sum of interior angles is given in the question so if we know about the number of sides then the name of a polygon can be determined.
Now, according to the question
The sum of interior angles = (n-2) x 180°
Now, as we know that the sum is 720°, putting the value we get
720° = (n – 2) x 180°
n – 2 = 720° / 180°
n - 2 = 4
n = 4 + 2
n = 6.
Thus, the name of a polygon is hexagon as the number of sides is equal to 6.
Ques. Find the sum of all the interior angles of a pentagon?
(a) 720°
(b) 540°
(c) 360°
(d) 180°
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Ans. (b) 540°
Explanation: As we know that the total number of sides of a pentagon is equal to 5, so we take n = 5.
The formula of all the sum of interior angles = (n - 2) x 180°
Now out the value of n in the formula we get
= (5 – 2) x 180°
= 540°
Hence, the sum of interior angles of a hexagon is 540°.
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