Answer:
1. Answer: (b) 10
Explanation: On the flip side, concave decagons have indentations, which create interior angles greater than 180º. Regardless of whether a decagon is concave or convex, it possesses the following qualities: It is a 10 sided shape. It has 10 vertices.
2. Answer: (d) 5
Explanation: Five measurements can determine a quadrilateral uniquely. A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal are given.
3. Answer: (c) perpendicular bisectors of
Explanation: The diagonals of a square bisect each other, are perpendicular to each other, and are of equal length.
4. Answer: (b) equal
Explanation: Opposite Angles of a Parallelogram are equal. By the ASA congruence criterion, two triangles are congruent to each other. Hence, it is proved that the opposite angles of a parallelogram are equal.
5. Answer: (c) 360º
Explanation: The sum of the measures of the angles of a convex quadrilateral is 360 as a convex quadrilateral is made of two triangles.If ABCD is a convex quadrilateral, made of two triangles ABD and BCD. Therefore, the sum of all the interior angles of this quadrilateral will be the same as the sum of all the interior angles of these two triangles i.e.,
180º + 180º = 360º
Yes, this property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.
6. Answer: (b) 9
Explanation: The number of diagonals of an n sided polygon is given by \(D_n=\frac{n(n-3)}{2}\)
A convex regular hexagon has 6 sides. So, n = 6
\(D_6=\frac{6(6-3)}{2}\)
= 9
7. Answer: (b) 60º
Explanation: Interior angle of an equilateral triangle is 60º, which is the minimum interior angle possible for the regular polygon.
8. Answer: (b) right
Explanation: The diagonals of a rhombus bisect each other at right angles.
9. Answer: (a) rectangle
Explanation: In a parallelogram, Both the pair of opposite sides are of equal length. Opposite angles are equal and two adjacent angles are supplementary. A rectangle is a parallelogram, in which each angle measures 90º. Hence, a parallelogram each of whose angle measures 90º is a rectangle.
10. Answer: (a) 24º
Explanation: The sum of the exterior angles of a regular polygon is 360º. The number of sides of polygon =15.
As each of the exterior angles is equal,
Exterior angle = 360º/15
= 24º
11. Answer: (d) 900º
Explanation: Sum of Interior Angles = (n−2)180º
Here n = Number of sides =7
Sum of interior angles = (7−2) ×180º
= 900º
12. Answer: (c) equal measure
Explanation: All angles of a regular polygon are equal in measure.
13. Answer: (d) concave
Explanation: A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex.
14. Answer: (c) triangle
Explanation: A polygon cannot be formed with just two lines or line segments. Hence, a minimum number of 3 lines or line segments are required to form a polygon. Such type of polygon is called a triangle.
15. Answer: (c) 3
Explanation: If we have the lengths of two adjacent sides, then since opposite sides are equal in a parallelogram, we have the lengths of the other sides too. Since opposite angles are equal, if one angle is known, we can figure out the remaining three as well. Thus, a minimum of three independent measurements are needed to construct a parallelogram.
16. Answer: (d) Only one side length
Explanation: A square has all its sides equal and all the interior angles measure 90 degrees. Hence, if the length of one side is known, then we can construct a square easily.
17. Answer: (c) Only Length and breadth
Explanation: A rectangle has its parallel sides equal and all the interior angles measure 90 degrees. Hence, if the length and breadth rectangle is known, then we can construct it easily.
18. Answer: (b) Pentagon
Explanation: By the angle sum of interior angles of a polygon, if n is the number of sides, then;
Sum of interior angles = (n-2) x 180°
540º = (n – 2) x 180º
n – 2 = 540º/180º = 3
n = 3 + 2
= 5
Thus, the polygon is a pentagon
19. Answer: (c) 20
Explanation: The formula to find the number of diagonals is:
D = n (n – 3)/2, where n is the number of sides
D = 8 ( 8 – 3)/2
D = 8 (5)/2
D = 20
20. Answer: (a) Yes
Explanation: A square has all its sides equal in length and all the angles are equal to 90 degrees. Therefore, we can take any five measurements to construct a square.
21. Answer: (c) centroid
Explanation: The centroid is the point of intersection of the medians in a triangle.
22. Answer: (a) circumcentre
Explanation: The three perpendicular bisectors of the sides of a triangle meet in a single point, called the circumcenter . A point where three or more lines intersect is called a point of concurrency.The circumcenter is equidistant from the vertices of the triangle.
23. Answer: (b) 8
Explanation: Euler's polyhedron formula, V− E + F = 2
V = number of vertices = 6
E = number of edges = 12
F = number of faces = ?
6 −12 + F = 2
F = 6 + 2
F = 8
Number of faces = 8
A octahederon has8 faces and 6 vertices with 12 edges.
24. Answer: (a) 9
Explanation: If F = faces,V = vertices,E = edges,
F + V−E = 2
i.e, 5 + 6− E = 2
E = 9.
25. Answer: (d) 4
Explanation: In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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