Respuesta :

linandrew41

In a parallelogram,

 ⇒the angles adjacent to each other

    ⇒ are of the same measure

        ⇒so

             ∠A = ∠C

             ∠B = ∠D

Let's solve:

  • ∠A = ∠C

           [tex]7z +5 = 8z - 10\\5+10=8z-7z\\8z-7z=5+10\\z = 15[/tex]

  •  ∠B = ∠D

           [tex]5w-30=3w+10\\5w-3w=30+10\\2w = 40\\w=20[/tex]

Let's check:

 ⇒ for all quadrilaterals like a parallelogram

    ⇒all the angle measures added up to 360, so:

     [tex](7z+5)+(8z-10)+(5w-30)+(3w+10)=360\\(7(15)+5)+(8(15)-10)+(5(20)-30)+(3(20)+10)=360\\(105+5)+(120-10)+(100-30)+(60+10)=360\\110+110+70+70=360\\220+140=360\\360=360[/tex]

Thus:

  Answer: w = 20 and z = 15

Hope that helps!    

It should be noted that the opposite angles of a parallelogram are equivalent. Therefore, ∠A = ∠C and ∠B = ∠D.

Given:

  • ∠A = 7z + 5
  • ∠B = 5w - 30
  • ∠C = 8z - 10
  • ∠D = 3w + 10

Therefore, we obtain the following equations;

⇒ 7z + 5 = 8z - 10   and   5w - 30 = 3w + 10

Let us simplify each equation one by one.

7z + 5 = 8z - 10:

  • ⇒ 7z + 5 = 8z - 10
  • ⇒ 7z + 5 - 5 = 8z - 10 - 5                 (Subtract 5 both sides)
  • ⇒ 7z = 8z - 15                                    (Simplify both sides)
  • ⇒ 7z - 8z = 8z - 15 - 8z                  (Subtract 8x both sides)
  • ⇒ z = 15                                              (Simplify both sides)

5w - 30 = 3w + 10:

  • ⇒ 5w - 30 = 3w + 10
  • ⇒ 5w - 30 - 3w = 3w + 10 - 3w      (Subtract 3w both sides)
  • ⇒ 2w - 30 = 10                                   (Simplify both sides)
  • ⇒ 2w - 30 + 30 = 10 + 30                   (Add 30 both sides)
  • ⇒ 2w = 40                                           (Simplify both sides)
  • ⇒ 2w/2 = 40/2                                    (Divide 2 both sides)
  • ⇒ w = 20                                             (Simplify both sides)

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