Maths-
General
Easy

Question

ABCD is a quadrilateral. AD and BD are the angle bisectors of angle A and B which meet at ‘O’. If angle C equals 70 to the power of ring operator end exponent comma angle D equals 50 to the power of ring operator end exponent. text  Find  end text angle A O B

  1. 40°    
  2. 60°    
  3. 80    
  4. 90°    

hintHint:

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees. Here we have given ABCD is a quadrilateral. AO and BO are the angle bisectors of angles A and B which meet at O. We have to find angle AOB.

The correct answer is: 60°


    A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are A, B, C, and D. A quadrilateral has the following sides: AB, BC, CD, and DA.
    We have given ABCD is a quadrilateral and AO and BO are the angle bisectors of angles A and B which meet at O.
    angle C equals 70 degree comma space angle D equals 50 degree
N o w space t h a t space A B C D space i s space a space q u a d r i l a t e r a l comma space s o colon
angle A plus angle B plus angle C plus angle D equals 360 degree space
left parenthesis A plus B right parenthesis equals 360 degree minus left parenthesis C plus D right parenthesis
left parenthesis A plus B right parenthesis equals 360 degree minus left parenthesis 70 degree plus 50 degree right parenthesis space space
left parenthesis A plus B right parenthesis equals 360 degree minus left parenthesis 70 degree plus 50 degree right parenthesis space space
left parenthesis A plus B right parenthesis equals 240 degree
N o w space w e space h a v e space g i v e n space t h a t space A O space a n d space B O space a r e space t h e space a n g l e space b i s e c t o r s space o f space a n g l e s space A space a n d space B space w h i c h space m e e t space a t space O comma space s o colon
angle O A B equals fraction numerator angle A over denominator 2 end fraction
angle O B A equals fraction numerator angle B over denominator 2 end fraction
N o w colon
angle O A B plus angle O B A equals fraction numerator angle A over denominator 2 end fraction plus fraction numerator angle B over denominator 2 end fraction equals 120 degree
S o space w e space h a v e space a n g l e space A O B space a s colon
angle A O B equals 180 degree minus 120 degree
angle A O B equals 60 degree

    So we have given a quadrilateral where we have AO and BO are the angle bisectors of angles A and B which meet at O. The measurements of the angles and side lengths of quadrilaterals are used to categorise them. So the angle AOB is 60 degree.

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