Mathematics
Grade-8
Easy

Question

Find the measure of all the angles.

  1. angle a equals 120 degree comma angle b equals 20 degree comma angle c equals 40 degree comma angle d equals 120 degree comma angle e equals 40 degree
  2. angle a equals 100 degree comma angle b equals 40 degree comma angle c equals 120 degree comma angle d equals 40 degree comma angle e equals 40 degree
  3. angle a equals 100 degree comma angle b equals 40 degree comma angle c equals 140 degree comma angle d equals 20 degree comma angle e equals 20 degree
  4. angle a equals 120 degree comma angle b equals 60 degree comma angle c equals 100 degree comma angle d equals 20 degree comma angle e equals 20 degree

hintHint:

In the triangle ABC,AB=AC
Angles opposite to equal sides are equal.

The correct answer is: angle a equals 100 degree comma angle b equals 40 degree comma angle c equals 140 degree comma angle d equals 20 degree comma angle e equals 20 degree


    In the triangle ABC,AB=AC
    Angles opposite to equal sides are equal.
    So, angle b=40
    and Then in the triangle ABC , the sum of the angles are 180
    angle a + angle b + 40=180
    angle a+40+40 =180
    angle a+80=180
    angle a=180-80
    angle a= 100
    WE know that angle b and angle c form a linear pair
    So, they are supplementary
    angle b +angle c=180
    40+angle c=180
    angle c=180-40
    angle c=140
    given that AB=BD
    We know that angles opposite to equal sides are equal.
    angle d= angle e
    now, angle b is the exterior angle of triangle ABD
    So, angle b=Angle d + angle e
    40=2*angle d
    angle d= 40/2
    angle d=20
    and angle e=20
    angle a equals 100 degree comma angle b equals 40 degree comma angle c equals 140 degree comma angle d equals 20 degree comma angle e equals 20 degree

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