Maths-
General
Easy

Question

In the given figure, find the values of x y, and z

  1. 84°, 68°, 90°    
  2. 88°, 104°, 92°    
  3. 88°, 78°, 100°    
  4. 88°, 68°, 92°    

hintHint:

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a 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 a figure and we have to find the values of x, y and z.
 

The correct answer is: 88°, 68°, 92°


    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.

    I n space t h i s space f i g u r e space w e space h a v e space g i v e n colon
angle F D C equals 112
angle D F E equals 70
angle D C E equals 90
N o w space w e space k n o w space a n g l e space s u m space p r o p e r t y space o f space q u a d r i l a t e r a l space i s space 360 space d e g r e e comma space s o colon
angle F E C equals 360 degree minus left parenthesis angle F D C plus angle D F E plus angle D C E right parenthesis
angle F E C equals 360 degree minus left parenthesis 112 plus 70 plus 90 right parenthesis
angle F E C equals 360 degree minus 272 degree
angle F E C equals 88 degree equals x
N o w space w e space c a n space s e e space t h a t space B E C space i s space a space s t r a i g h t space l i n e comma space s o space a n g l e space B E F space a n d space F E C space a r e space l i n e a r space p a i r s. space
angle B E F plus angle F E C equals 180 degree
angle B E F equals 180 degree minus 88 degree
angle B E F equals 92 degree equals z
N o w space w e space c a n space s e e space t h a t space A F D space i s space a space s t r a i g h t space l i n e comma space s o space a n g l e space A F E space a n d space E F D space a r e space l i n e a r space p a i r s. space
angle A F E plus angle E F D equals 180 degree
angle A F E equals 180 degree minus 70 degree
angle A F E equals 110 degree
N o w space w e space k n o w space a n g l e space s u m space p r o p e r t y space o f space q u a d r i l a t e r a l space i s space 360 space d e g r e e comma space s o colon
angle F A B equals 360 degree minus left parenthesis angle A B E plus angle B E F plus angle E F A right parenthesis
angle F A B equals 360 degree minus left parenthesis 90 plus 92 plus 110 right parenthesis
angle F A B equals 360 degree minus 292 degree
angle F A B equals 68 degree equals y

    So we have given a quadrilateral where we have to find the angles x, y and z. The measurements of the angles and side lengths of quadrilaterals are used to categorise them. So the values of x, y and z are: 88°, 68°, 92°

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