Respuesta :

reinhard10158

Step-by-step explanation:

who wrote all the 45° angles there ?

if that were correct angles than the rectangle would be a square, and the angles between the diagonals would be 90° (an angle of 116° would be impossible there).

so, this is all wrong.

a rectangle has 4 vertices. each one has an inner angle of 90°.

so,

angle 1 + angle 4 = 90°

angle 6 + angle 7 = 90°

the diagonals split the angles at the end points of the diagonals in an equal way - just up-down mirrored.

so,

angle 6 = angle 3

angle 1 = angle 5

as the diagonals are congruent, also the neighboring angles are equal (similarly left-right mirrored).

angle 3 = angle 4

angle 1 = angle 7 = angle 5

the sum of all angles around a single point on one side of a line is always 180° (see the line as diameter of an invisible circle with the point being its center : then each side of the line represents a half-circle, and a half-circle stands for 180°).

so,

angle 2 + 116° = 180°

angle 2 = 180° - 116° = 64°

the sum of all angles in a triangle is always 180° too.

so,

angle 2 + angle 3 + angle 4 = 180°

remember, angle 3 = angle 4

so,

64° + 2×angle 3 = 180°

2×angle 3 = 180° - 64° = 116°

angle 3 = angle 4 = angle 6 = 116/2 = 58°

remember

angle 4 + angle 1 = 90°

58° + angle 1 = 90°

angle 1 = angle 5 = angle 7 = 90 - 58 = 32°

FYI : in a rectangle the diagonals do usually not split the angles at the vertices in half. only in squares (as a special form of rectangles).

devishri1977

Answer:

Linear pair: If the non-common arms of two adjacent angles form a straight line, then the two adjacent angles are called linear pair and they add up to 180°.

     116° + ∠2 = 180°

               ∠2 = 180 - 116

               ∠2 = 64°

In a rectangle the diagonals are equal, and they bisect each other.

Let the diagonals BD and AC bisect at O.

BO = OD = AO = CO.

In ΔBOC,

     BO = CO.

⇒ΔBOC is an isosceles triangle.

∴ ∠4 = ∠3 = x

x + x + ∠2 = 180 {angle sum property of triangle}

    2x + 64 = 180

            2x = 180 - 64

             2x = 116

               x = 116 ÷ 2

                x = 58°

[tex]\boxed{\bf \angle4 = \angle 3 = 58^\circ}[/tex]

We know that ∠C = 90°

     ∠C = 90°

∠1 + ∠4 = 90

  ∠1 + 58 = 90

            ∠1 = 90 - 58

             [tex]\boxed{\bf \angle 1 = 32^\circ}[/tex]

 ΔDOC is isosceles triangle.

       ∠7 = ∠1

         [tex]\boxed{\bf \angle 7 = 32^\circ}[/tex]

∠D = 90

∠6 + ∠7 = 90

 ∠6 + 32 = 90

          ∠6 = 90 - 32

           [tex]\boxed{\bf \angle6 = 58^\circ}[/tex]

AB // CD, AC is transversal.

 ∠5 = ∠1 {Alternate interior angles}

   [tex]\boxed{\bf \angle 5 = 32^\circ}[/tex]

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