Plane Geometry

Plane Geometry

Easy Questions
Moderate Questions
Difficult Questions
Plane Geometry Tutorial

Aptitude

Simplification
Number System
Fractions
Elementary Algebra
LCM and HCF
Approximation
Unitary Method
Linear Equation
Quadratic Equation
Discount
Average
Surds and Indices
Percentage
Square root and cube root
Order of Magnitude
Work and Wages
Odd Man Out and Series
Algebra
Profit and Loss
Stocks and Shares
True Discount
Ratio, Proportion
Partnership
Alligation or Mixture
Time and Work
Pipes and Cistern
Speed, Time and Distance
Problem on Trains
Height and Distance
Banker's Discount
Boats and Streams
Races and games
Problems on Ages
Clocks and Calendars
Simple interest
Compound Interest
Sets and Functions
Area and Perimeter
Volume and Surface Area of Solid Figures
Sequences and Series
Plane Geometry
Logarithm
Probability
Permutation and Combination
Statistics
Mensuration
Trigonometry
Aptitude miscellaneous
  1. An interior angle of a regular polygon is 5 times its exterior angle. Then the number of sides of the polygon is








  1. View Hint View Answer Discuss in Forum

    If the number of sides of regular polygon be n, then

    Each interior angle =
    (2n - 4) × 90°
    n

    And each exterior angle =
    360°
    n

    According to question ,
    ∴
    (2n - 4)
    		 × 90° =
    5 × 360°
    nn

    ⇒ (2n – 4) = 5 × 4
    ⇒ 2n – 4 = 20

    Correct Option: C

    If the number of sides of regular polygon be n, then

    Each interior angle =
    (2n - 4) × 90°
    n

    And each exterior angle =
    360°
    n

    According to question ,
    ∴
    (2n - 4)
    		 × 90° =
    5 × 360°
    nn

    ⇒ (2n – 4) = 5 × 4
    ⇒ 2n – 4 = 20
    ⇒ 2n = 20 + 4 = 24
    ⇒ n =
    24
    		 = 12
    2

  1. The interior angle of a regular polygon is 140°. The number of sides of that polygon is








  1. View Hint View Answer Discuss in Forum

    ∴ An interior angle of a regular polygon =
    (2n - 4) × 90°
    n

    Where n = number of sides
    Given , The interior angle of a regular polygon = 140
    ∴
    (2n - 4) 90°
    		 = 140
    n

    ⇒ 9 (2n – 4) = 14n
    ⇒ 18n – 36 = 14n
    ⇒ 18n – 14n = 36
    ⇒ 4n = 36

    Correct Option: A

    ∴ An interior angle of a regular polygon =
    (2n - 4) × 90°
    n

    Where n = number of sides
    Given , The interior angle of a regular polygon = 140
    ∴
    (2n - 4) 90°
    		 = 140
    n

    ⇒ 9 (2n – 4) = 14n
    ⇒ 18n – 36 = 14n
    ⇒ 18n – 14n = 36
    ⇒ 4n = 36
    ⇒ n =
    36
    		 = 9
    4

  1. In a regular polygon if one of its internal angle is greater than the external angle by 132°, then the number of sides of the polygon is








  1. View Hint View Answer Discuss in Forum

    Let Number of sides of regular polygon = n
    According to question ,

    ∴
    (2n - 4) × 90°
    		 -
    360°
    		 = 132°
    nn

    ⇒ 180n – 360 – 360 = 132n

    Correct Option: C

    Let Number of sides of regular polygon = n
    According to question ,

    ∴
    (2n - 4) × 90°
    		 -
    360°
    		 = 132°
    nn

    ⇒ 180n – 360 – 360 = 132n
    ⇒ 180n – 132n = 720
    ⇒ 48n = 720
    ⇒ n =
    720
    		 = 15
    48

  1. The sum of all internal angles of a regular polygon whose one external angle is 20° is








  1. View Hint View Answer Discuss in Forum

    Here , External angle = 20°

    Number of sides of a regular polygon (n) =
    360
    		 = 18
    20

    ∴ Sum of all interior angles = (2n – 4) × 90°

    Correct Option: C

    Here , External angle = 20°

    Number of sides of a regular polygon (n) =
    360
    		 = 18
    20

    ∴ Sum of all interior angles = (2n – 4) × 90°
    Sum of all interior angles = (2 × 18 – 4) × 90°
    Sum of all interior angles = 32 × 90° = 2880°

  1. The sum of the internal angles of a regular polygon is 1440° The number of sides is








  1. View Hint View Answer Discuss in Forum

    Let the number of sides of regular polygon be n.
    ∴ Sum of all interior angles = (2n – 4) × 90°
    According to question ,
    The sum of the internal angles = 1440°
    ⇒ (2n – 4) × 90° = 1440°
    ⇒ (2n – 4) = 1440° ÷ 90° = 16
    ⇒ 2n – 4 = 16

    Correct Option: B

    Let the number of sides of regular polygon be n.
    ∴ Sum of all interior angles = (2n – 4) × 90°
    According to question ,
    The sum of the internal angles = 1440°
    ⇒ (2n – 4) × 90° = 1440°
    ⇒ (2n – 4) = 1440° ÷ 90° = 16
    ⇒ 2n – 4 = 16
    ⇒ 2n = 16 + 4 = 20
    ⇒ n = 20 ÷ 2 = 10