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Q1. For a rhombus, which of the following statement is correct?

• Opposite sides and angles are equal
• Diagonals are equal
• Each of the angles is a right angle
• Diagonals do not bisect each other

Solution

A rhombus has all the properties of a parallelogram. Hence,  opposite sides and opposite angles are equal in a rhombus. Also diagonals bisect each other but they are not equal.

Q2. Sum of all interior angles of a convex polygon with five sides is

• 540^o
• 360^o
• 720^o
• 180^o

Solution

We know that the sum of the interior angles of a polygon of n sides is equal to (n - 2) 180^o. So, the sum of all interior angles of a convex polygon with five sides = (5 - 2) x 180^o = 3 x 180^o = 540^o

Q3. Angle sum is 360^o in

• Rhombus and Kite
• Rectangle and Prallelogram
• Kite and Square
• All of the above

Solution

The sum of all angles of a quadrilaterals is 360^o. And, Rhombus, Kite, Rectangle, Parallelogram, Square are all quadrilaterals. 

Q4. If two angles of a quadrilateral are 45^o and 75^o, sum of the other two angles is

• 240^o
• 120^o
• 360^o
• 180^o

Solution

The sum of all angles of a quadrilateral is 360^o. Hence, sum of the other two angles = 360^o - (45^o + 75^o) = 360^o - 120^o = 240^o

Q5. Which of the following is not a property of a parallelogram?

• Opposite angles are equal
• Opposite sides are equal
• Diagonals are perpendicular to each other
• Diagonals bisect each other

Solution

In a parallelogram, diagonals bisect each other but they are not perpendicular.

Q6. A square is a

• Rectangle with each angle = 90^o
• Rhombus with all equal sides
• Parallelogram with opposite sides equal and parallel
• All of the above.

Solution

Each angle of a square is a right angle, so it is a rectangle. All the sides of a square are equal, so it is a rhombus. The opposite sides of a square are equal and parallel, so it is a parallelogram.

Q7. A triangle with two angle each of 90^o and 60^o, has its third angle equal to

• 30^o
• 40^o
• 60^o
• 80^o

Solution

The sum of angles of a triangle is 180^o. Hence, measure of third angle = 180^o - 90^o - 60^o = 30^o

Q8. Sum of all interior angles of a nonagon is

• 1620^o
• 1080^o
• 1460^o
• 1260^o

Solution

Sum of all interior angles of a polygon with n sides = (n - 2) × 180^o Now, nonagon has 9 sides. Therefore, sum of all interior angles of a nonagon = (9 - 2) × 180^o= 7 × 180^o = 1260^o

Q9. Kite and trapezium are

• polygons
• simple open curves
• parallelograms
• made up of arcs

Solution

Kite and trapezium are polygons (simple closed curves made of line segments).

Q10. How many diagonals are there in a triangle?

• 1
• 2
• 3
• zero

Solution

A triangle does not have a diagonal as its each vertex is adjacent to the other two.

Q11. How many sides a heptagon has?  

• 6
• 7
• 8
• 4

Solution

A heptagon has 7 sides.

Q12. Opposite sides are not equal in

• Rhombus
• Rectangle
• Square
• kite

Solution

Opposite sides are equal and parallel in all the parallelograms but not in a kite. So, the correct answer is Kite.

Q13. In which of the following quadrilaterals, diagonals do not bisect each other?

• Square
• Rectangle
• Rhombus
• Kite

Solution

In kite, only one of the two diagonals is bisected, while in others both diagonals are bisected.

Q14. A concave polygon can be made with minimum of

• 4 line segments
• 6 line segments
• 3 line segments
• 5 line segments

Solution

A concave polygon is defined as a polygon with one or more interior angles greater than 180°. Hence, we need at least 4 line segments to make a concave polygon.

Q15. A quadrilateral with only one pair of parallel sides is a 

• parallelogram
• kite
• trapezium
• square

Solution

Trapezium has only one pair of parallel sides.

Q16. Adjacent sides and adjacent angles are equal in 

• Square
• Rhombus
• Rectangle
• Kite

Solution

For a Square, adjacent sides and adjacent angles are equal. 

Q17. A regular polygon of three sides is a /an _______ triangle.

• Isosceles
• Equilateral
• Scalene
• None of the Above

Solution

An equilateral triangle is a regular polygon of 3 sides.

Q18. The measure of each exterior angle of a regular polygon of 12 sides is

• 30^o
• 60^o
• 45^o
• 75^o

Solution

Q19. A kite has

• five equal sides
• three pairs of equal consecutive sides
• two pair of parallel sides
• two pairs of equal consecutive sides

Solution

A kite has two pairs of equal consecutive sides.

Q20. Diagonals do not bisect each other in

• Rhombus
• Kite
• Rectangle
• Square

Solution

Diagonals do not bisect each other in kite. In kite, only one of the two diagonals is bisected.

Q21. The number of vertices of a pentagon is

• 5
• 6
• 7
• 8

Solution

A pentagon has 5 sides and 5 vertices.

Q22. An octagon is made up of ______ sides.

• 8
• 10
• 6
• 5

Solution

An octagon is made up of 8 sides.

Q23. The adjacent angles in a parallelogram are 

• supplementary
• equal
• complementary
• not equal

Solution

The adjacent angles of a parallelogram are supplementary.

Q24. If three angles of a quadrilateral are 50^o, 70^o and 120^o, then the fourth angle of the quadrilateral is

• 60^o
• 180^o
• 120^o
• 240^o

Solution

The sum of the angles of a quadrilateral is 360^o. Hence, Fourth angle = 360^o - (50^o + 70^o + 120^o) = 360^o - 240^o = 120^o

Q25. If a + 10^o, 3a + 10^o, 5a - 10^o and 3a - 10^o are the angles of a quadrilateral, then what is the value of a?

• 20^o
• 30^o
• 40^o
• 50^o

Solution

Given, a + 10^o, 3a + 10^o, 5a - 10^o and 3a - 10^o are the angles of a quadrilateral. We know that the sum of the angles of a quadrilateral is 360^o. Therefore, a + 10^o + 3a + 10^o + 5a - 10^o + 3a - 10^o = 360^o 12a = 360^o a = 30^o

Q26. Which of the following quadrilaterals is not a parallelogram?

• Square
• Rectangle
• Rhombus
• Kite

Solution

Kite is not a parallelogram since its opposite sides are not parallel.

Q27. Diagonals are of equal length in

• Rectangle and Square
• Rhombus and Rectangle
• Square and Rhombus
• Kite and Rhombus

Solution

In a Rectangle and Square, both diagonals are of equal length.

Q28. Quadrilaterals with four right angles are

• Square and Rectangle
• Rectangle and Rhombus
• Rhombus and Kite
• Trapezium and Square

Solution

Each angle of Square and Rectangle is equal to 90^o.

Q29. In □LMNO, if m ∠L = 100° and m ∠M = 80°, then m ∠N +m ∠O =?

• 270°
• 180°
• 90°
• 360°

Solution

The sum of angles of a quadrilateral is 360^o. m∠L +m ∠M = 100° + 80° = 180°  ∴m ∠N +m ∠O = 180° 

Q30. If two adjacent angles of a parallelogram are equal, then it is a 

• rectangle or rhombus
• rectangle or square
• square or rhombus
• kite or rhombus

Solution

In a rectangle as well as in square, each angle is 90^o, so their adjacent angles are supplementary as well as equal.

Q31. What kind of polygon is a rectangle?

• Irregular
• Convex
• Quadrilateral
• All of the above

Solution

A rectangle is a convex quadrilateral. Since all the sides of a rectangle are not equal, it is irregular also.

Q32. The measure of each interior angle of a regular nonagon is

• 40^o
• 140^o
• 90^o
• 180^o

Solution

The sum of the interior angles of a polygon with n sides = (n - 2) × 180^o  A nonagon has 9 sides. Therefore, sum of interior angles of a nonagon = (9 - 2) × 180^o = 7 × 180^o = 1260^o

Q33. Which one of the following is not a parallelogram?

• Rhombus
• Trapezium
• Rectangle
• Square

Solution

Trapezium is not a parallelogram as it has only one pair of parallel sides.

Q34. If all angles of a parallelogram are 90^o, then it can either be a _________ or a ____________.

• Rectangle, Rhombus
• Rectangle, Square
• Square, Rhombus
• None of the Above

Solution

All angles of rectangle and square are 90^o.

Q35. Which of the following is not a polygon?

• Triangle
• Circle
• Kite
• Quadrilateral

Solution

Since, a polygon is a closed curve made up of only line segments, a circle is not a polygon. 

Q36. Sum of the measure of the exterior angles of a decagon is 

• 180^o
• 360^o
• 270^o
• 90^o

Solution

Sum of the measures of the exterior angles of any polygon is 360^o.

Q37. Third exterior angle of a triangle with two exterior angles 90^o and 135^o is 

• 135^o
• 65^o
• 105^o
• 95^o

Solution

We know that sum of all the three exterior angles of a triangle is 360^o. Therefore, 90^o + 135^o + Third exterior angle = 360^o or 225^o + Third exterior angle = 360^o or Third exterior angle = 360^o - 225^o = 135^o

Q38. Among the following properties, which are not true for a polygon?

• Curve
• Simple
• Made of line segments
• Open

Solution

A simple closed curve made up of only line segments is called a polygon.

Q39. A polygon should have at least   

• 4 sides
• 2 sides
• 3 sides
• 5 sides

Solution

Since we cannot form a closed curve from less than 3 line segments. Hence, a polygon should have at least 3 sides to be a closed curve.

Q40. Minimum interior angle possible for a regular polygon is 

• 60^o
• 120^o
• 45^o
• 90^o