Rectilinear Figures

A plane figure bounded by line segments is called a rectilinear figure.

A closed plane geometrical figure bounded by at least 3 line segments is called a polygon.

The line segments forming a polygon intersect only at end-points and each end-point is shared by only two line segments.

On the basis of sides, the polygons are classified as triangles, quadrilaterals, pentagons, hexagons, etc.

A convex polygon is defined as a polygon with each of its interior angles less than 180°.

A concave polygon is defined as a polygon with one or more interior angles greater than 180°.

A polygon is said to be a regular polygon, if all its interior angles are equal, sides are equal and exterior angles are equal.

The sum of all the interior angles of a convex polygon of n sides is (2n – 4) right angles.

Each interior angle (Regular Polygon) = [(2n – 4) / n] right angles

= [{(2n – 4) × 90} / n]°

The sum of all the exterior angles of a convex polygon of n sides is 4 right angles.

Each exterior angle of a regular polygon with n sides = 360° / n

Greater the number of sides in a regular polygon, greater is the value of its each interior angle and smaller is the value of its each exterior angle.

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  • Q1

    Find the number of sides of a regular polygon whose each exterior angle has a measure of 60.

    Marks:2
    Answer:

    Total measure of all exterior angles = 360

    Measure of each angle = 60
    Therefore, the number of exterior angles =

    Hence, the polygon has 6 sides.

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  • Q2

    What is the sum of all exterior angles of a polygon of n sides?

    Marks:1
    Answer:

    Sum of all exterior angles of a polygon of n sides is 360°.

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  • Q3

    How many vertices are there in a nonagon?

    Marks:1
    Answer:

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  • Q4

    Write the formula of sum of all interior angles of a polygon of n sides.

    Marks:1
    Answer:

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  • Q5

    What is a concave polygon?

    Marks:1
    Answer:

    If at least one angle of a polygon is more than 180°, then it is called a concave polygon.

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