Plane Geometry
- The sum of interior angles of a regular polygon is 1440°. The number of sides of the polygon is
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If the number of sides of regular polygon be n, then
The sum of interior angles of a regular polygon = 1440°
⇒ (2n – 4) × 90° = 1440°⇒ 2n - 4 = 1440 = 16 90
⇒ 2n – 4 = 16
Correct Option: A
If the number of sides of regular polygon be n, then
The sum of interior angles of a regular polygon = 1440°
⇒ (2n – 4) × 90° = 1440°⇒ 2n - 4 = 1440 = 16 90
⇒ 2n – 4 = 16
⇒ 2n = 20
⇒ n = 10
- A polygon has 54 diagonals. The number of sides in the polygonis
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We can find required answer with the help of given formula ,
Number of diagonals = n(n - 3) 2
From question ,54 = n(n - 3) 2
Correct Option: C
We can find required answer with the help of given formula ,
Number of diagonals = n(n - 3) 2
From question ,54 = n(n - 3) 2
⇒ n(n – 3) = 108 = 12 × 9
⇒ n (n – 3) = 12 ( 12 – 3)
⇒ n = 12
Hence , Number of diagonals = 12
- Two regular polygons are such that the ratio between their number of sides is 1 : 2 and the ratio of measures of their interior angles is 3 : 4. Then the number of sides of each polygon is
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Given , The ratio between their number of sides = 1 : 2
and the ratio of measures of their interior angles = 3 : 4.
As we know that ,Each interior angle of n –sided polygon = 2n - 4 right angles n
According to the question,2 × y - 4 y = 3 2 × 2y - 4 4 2y ⇒ 2y - 4 × 2y = 3 y 4y - 4 4 = 4y - 8 = 3 y - 1
Correct Option: D
Given , The ratio between their number of sides = 1 : 2
and the ratio of measures of their interior angles = 3 : 4.
As we know that ,Each interior angle of n –sided polygon = 2n - 4 right angles n
According to the question,2 × y - 4 y = 3 2 × 2y - 4 4 2y ⇒ 2y - 4 × 2y = 3 y 4y - 4 4 = 4y - 8 = 3 y - 1
⇒ 4y – 8 = 3y – 3
⇒ 4y – 3y = 8 – 3
⇒ y = 5
∴ Number of sides of polygons = 5 and 10.
- If an interior of a regular polygon is 170°, then the number of sides of the polygon is
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Here , An interior of a regular polygon = 170°
we know that ,Each interior angle of regular polygon = 
2n - 4 
× 90° n
where, n = number of sides∴ 2n - 4 × 90° = 170° n
Correct Option: A
Here , An interior of a regular polygon = 170°
we know that ,Each interior angle of regular polygon = 2n - 4 × 90° n
where, n = number of sides∴ 2n - 4 × 90° = 170° n ⇒ (2n - 4) × 9 = 17 n
⇒ 18n – 36 = 17n
⇒ 18n – 17n = 36
⇒ n = 36
- The length of the diagonal BD of the parallelogram ABCD is 18 cm. If P and Q are the centroid of the ;∆ ABC and ∆ ADC respectively then the length of the line segment PQ is
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According to question , we draw a figure of parallelogram ABCD ,
Centroid is the point where medians intersect. Diagonals of parallelogram bisect each other.OP = 1 × 9 = 3cm 3
Correct Option: B
According to question , we draw a figure of parallelogram ABCD ,
Centroid is the point where medians intersect. Diagonals of parallelogram bisect each other.OP = 1 × 9 = 3cm 3 OQ = 1 × 9 = 3cm 3
∴ PQ = OP + OQ = 3 + 3 = 6cm
