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Angles | O Level Mathematics 4024 & IGCSE Mathematics 0580 | Detailed Free Notes To Score An A Star (A*)

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  • Angles at a point
    • The total angle in the complete circular form is 360 degree.
    • All angles that we add at any point will be 360 degree
    • The total angle on a straight line is 180 degree.
    • The total angle where we have a perpendicular line is 90 degree.
      • 90 degree means that one line is perpendicular to another
    • Remember
      • Bisector is a line that divides another line into two equal halves
      • Perpendicular bisector is a line that divides another line into two equal halves and creates angles of 90 degree as well.
  • Angles formed when two parallel lines intersect each other
    • Parallel lines have the same gradient.
      • They will never touch each other no matter how much we extend each line.
    • Here, there are two sets of parallel lines, let’s call them A B C D
    • Here, A and B are parallel
    • C and D are parallel
    • Here, some angles are equal to each other.
    • There two angles are equal
    • There two angles are equal as well
    • These two angles are equal as well
    • These two angles are equal as well.
  • Also, wherever we form a Z, we also have same angles
    • These two angles are equal as well.
  • Angle properties of triangles
    • The total angles of triangle is 180 degree
    • In a right angled triangle, one angle is of 90 degree
      • The other two angles are less than 90 degree each.
    • In an acute angled triangle
      • All three angles are less than 90 degrees.
    • In an obtuse angled triangle
      • One angle is greater than 90 degree
      • Other two angles are all than 90 degree each.
  • Square
    • All 4 angles are of 90 degrees
  • Rectangle
    • All 4 angles are of 90 degrees
  • Polygon
    • A shape with multiple sides.
  • Regular Polygons
    • A polygon where all the interior angles are equal.
    • Interior angles
      • Angles inside the polygon
    • Here, we use the following formula
      • A single interior angle of a regular polygon = total sum of interior angles / number of sides
    • The sum of exterior angles (angles that are outside the polygon) is 360 degree.
    • The length of each side are equal
  • Irregular polygons
    • The interior angles of a polygon are not equal
    • Their lengths are also not equal
  • Angle of Semi Circle
    • A semi circle is one that has been divided from the middle
    • Therefore, the straight line at the bottom of the semi circle is the diameter
    • The circumference is half.
  • Angle between a tangent and radius of a circle
    • Tangent is a line that just touches the circumference of a circle at one single point
    • The angle between radius and the tangent is 90 degree or right angle

Circle Properties

Courtesy Math Tutor

  • Cord
    • A line that touches the circle’s circumference at two points, but does not pass through the center.
    • If it pass through the center, then it is called diameter
  • Top left
    • The angle at center is two times the angle at the circumference if made from the same cord
  • First row, second one
    • The angle made from the same cord on the same side of the circumference at two different points is the same
  • First row, third one
    • Angle made by diameter at the circumference is a 90 degree or right angle
  • First row, Fourth One
    • Angle made by radius on the tangent is on 90 degree or right angle
  • Second row, first one
    • A cyclic quadrilateral is one that has four angles made at the circumference.
    • The alternative angles in a cyclic quadrilateral have a sum of 180 degree
    • Alternative angle means one angle, then leave the next angle in clockwise/ anticlockwise movement, and then the next angle.
  • Second row, second one
    • Radius touching a cord is a perpendicular bisector
    • Divides in two equal parts and makes an angle of 90 degree or right angle.
  • Second row, Third one
    • Two tangents originating form the same point make the same angle on the circle
    • They also make the same angles
  • Second row, Fourth one
    • To cord that are on the same distant from the center have the same length to each other
  • The rest three are not that important
Hunain Zia

Hunain Zia has previously achieved considerable success in the high-school educational stream, gaining a massive 154 Total A Grades and 7 Major Distinctions, a process in which he broke/ set 11 different world records, including the most A grades ever achieved, most subjects ever appeared in, most distinctions, gaining distinctions across two separate boards (Pearson Edexcel and CAIE) within the same year/ ever, and even 19 hours of constant examination. All records stand intact today. Hunain pursued his Honors Accounting Degree from the prestigious Bentley University, and then completed an LLB (in Honors) from University of London. Currently, he manages multiple social and commercial projects, has founded digital streams and works tirelessly in the education sector.

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