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The value of x is ,  as these are the corresponding angles.
The given angles are linear pair of angle as they form a straight line.
The linear pair of the  is :                Thus the value of x is :                                        (Corresponding angles of parallel lines are equal).
The angles can be found using different properties: (a)         (The angles are linear pair) (b)                              (Vertically opposite angle) (c)                                            (Corresponding angle) (d)                             (Vertically opposite angle) (e)              (Vertically opposite angel,  linear pair).
The angles shown are pair of alternate interior angles.
These are pair of corresponding angles.
(i) Corresponding angles :-    ,  ,  ,   (ii) Alternate interior angles :-    ,  ,   (iii) Alternate angles on the same side of traversal :-   ,   (iv) Vertically opposite angles :-       , ,  ,
The angles shown are pair of interior angles.
The given pair of angles are alternate interior angles.
The property used here is 'Interior angles on the same side of the transversal are a pair of supplementary angles'.
The given pair of angles are corresponding angles.
The property used here is 'alternate interior angle property'.
The statement  "If  , then   "  is true using the corresponding angles property.
Few examples of the transversal are road crossing of different railway line crossing the other lines. Transversal intersects lines at a distinct point.
We know that transversal cuts lines at distinct points. Thus if a transversal cuts 3 lines then it will have 3 intersecting points.
We can draw infinite transversals from these two lines.
No, it is not necessary that lines always intersect at right angles. The lines may form an acute angle (another angle will be obtuse as to form linear pair).
We know that the opposite sides of the rectangle are equal and parallel to each other. Then for two interior angles on the same side of the transversal, we can write :                                       Also,                                          (Since opposite sides are equal) Thus
(i)   are the vertically obtuse angles.  (ii)   are the complementary angles. (iii)   are the equal supplementary angles. (iv)   are the unequal pair of supplementary angle. (v)  ,   and   are adjacent angles but are not supplementary angles.
We know that the sides of the equilateral triangle are equal. Consider an equilateral triangle ABC. Then                    So,                       or                                                    or                                                      Hence angles of an equilateral triangle are .
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