Angles

In geometry, an angle can be defined as the figure formed by two straight lines meeting at a common end point.

An angle is represented by the symbol ∠. Here, the angle below is ∠AOB.

Parts of an Angle:

Arms: The two rays joining to form an angle are called arms of an angle. Here, OA and OB are the arms of the ∠AOB.

Vertex: The common end point at which the two rays meet to form an angle is called the vertex. Here, the point O is the vertex of ∠AOB.

 

Types of angle

Angles can be classified on the basis of their measurements as

An acute Angle is an angle that measures less than 90 degrees

A right Angle is an angle which is equal to 90°,

An obtuse Angle is  an angle has a measurement greater than 90 degrees but less than 180 degrees.

A straight Angles is an angle is 180 degrees

A reflex Angles is an angle that is more than 180deg but less than 360deg

A complete Angle is a straight line makes an angle of 360∘

Interior and Exterior Angles:

Interior angle

• An interior angle of a polygon is an angle inside the polygon at one of its vertices.
• The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180.
• The measure of each interior angle of an equiangular n-gon is 180(n -2) /n

 

 Exterior angle 

• An exterior angle of a polygon is an angle outside the polygon formed by one of its sides and the extension of an adjacent side.
• If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.
• The measure of each exterior angle of an equiangular n-gon is 360 /n

Terms related to sum of angles

Complementary angles add up to 90⁰

Supplementary angles add up to 180⁰

 

Polygons

Polygons are usually defined by the number of sides that they have.

• A triangle

Is a three-sided polygon. Triangles can be defined by the length of the sides.

• Equilateral triangle has all sides equal and all its internal angles are 60⁰.
• Isosceles triangle has two equal sides, with the third one a different length. Two of the internal angles are equal
• Scalene triangle has all the three sides and all the three internal angles different
• Right angled triangle has one of the angle = 90⁰
• All internal angles of triangles add up to 180⁰.

Quadrilaterals

This are four-sided polygons

The internal angles of all quadrilaterals add up to 360⁰.

They include the square, rectangle, rhombus, parallelograms, trapezium and kite

• Square: all its sides are equal and each of its internal angles is equal to 900
• Rectangle: has four internal angles each equal to 900 and equal opposite sides
• Parallelogram has equal opposite sides and angles
• Rhombus has all sides equal and equal opposite angles
• Trapezium: has two parallel sides and unequal angle
• Kite has two pairs of equal adjacent sides, the shape has an axis of symmetry

Parallel lines

These are lines that are always same distance apart and will never meet.

Transversal line is a line that cuts through two or more parallel lines

The following about parallel lines are equal

 

 

For revision question download PDF below

lines, Angle, polygonss- upper primary

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