Maths-
General
Easy

Question

In the fig. ‘O’ is the centre of Circle. Chords AC and BD intersect at right angles at E, if stack ∣ O A B with _ below= 35° then left floor E B C equals

  1. 35°    
  2. 45°    
  3. 40°    
  4. 50°    

Hint:

The fundamental geometric shapes are lines and angles. Infinite points that stretch infinity in both directions make up lines, which are geometric objects. Straight lines with little depth or width are present. Here we have given a figure and ‘O’ is the centre of Circle. Chords AC and BD intersect at right angles at E. We have to find the angle EBC.

The correct answer is: 35°


    A line is a simple, one-dimensional shape that can go on forever in opposing directions. A line may be vertical or horizontal. It can be drawn either top to bottom or left to right.
    When the ends of two rays collide at a single location, an angle is a geometry that results. They are expressed as radians or degrees (°). A 360-degree angle is the same as a whole rotation. It is symbolized by the character "∠".
    If a triangle side is created, the outside angle that results is equal to the product of the two opposite internal angles.

    H e r e space O A space a n d space O B space a r e space r a d i i space o f space t h e space c i r c l e comma space s o space A O B space i s space a n space i s o s c e l e s space t r i a n g l e. space
S o space w e space g e t space space
angle O B A equals angle O A B equals 25 degree space space space space
N o w space u sin g space t h e space a n g l e space s u m space p r o p e r t y space o f space t r i a n g l e comma space w e space g e t colon space space space
angle O A B plus angle O B A plus angle A O B equals 180 degree space space space
35 degree space plus 35 degree space plus angle A O B equals 180 degree space
angle A O B equals 180 degree minus 70 degree
angle A O B equals 110 degree
W e space a r e space a w a r e space t h a t space a n space a r c apostrophe s space a n g l e space a t space i t s space c e n t r e space i s space t w i c e space a s space l a r g e space a s space i t s space a n g l e space a t space a n y space o t h e r space p o i n t space o n space i t s space c i r c u m f e r e n c e.
S o space w e space g e t space colon
angle A O B equals 2 cross times angle A C B space space
N o w space w e space c a n space w r i t e space i t space a s colon space
angle A C B equals fraction numerator angle A O B over denominator 2 end fraction space space
P u t t i n g space t h e space v a l u e s comma space w e space g e t colon
angle A C B equals fraction numerator 110 degree over denominator 2 end fraction space space
angle A C B equals 55 degree
N o w space c o n s i d e r space triangle B E C comma space u sin g space a n g l e space s u m space p r o p e r t y space o f space a space t r i a n g l e comma space w e space g e t colon
angle E B C plus angle B E C plus angle E C B equals 180 degree
P u t t i n g space t h e space v a l u e s comma space w e space g e t colon
angle E B C plus 90 degree space space plus 55 degree space space equals 180 degree
angle E B C equals 180 degree minus 145 degree
angle E B C equals 35 degree

    Here we used the concept of angle sum property of a triangle. When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. So here the angle EBC is 35 degree.

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