Question

Need answers to number 11 and step by step please Much appreciated thank you

Answer 1

Answer:

∠1 = 43

∠2 = 17

∠3 = 120

∠4 = 60

∠5 = 60

∠6 = 60

∠7 = 17

∠8 = 120

∠9 = 43

Step-by-step explanation:

11) ΔABC is isosceles triangle. In isosceles triangle two sides are equal and angles opposite to two sides are equal  {Isosceles triangle property}

∠C = ∠A

      9x - 47 =  4x + 3

9x - 4x - 47 = 3

     5x - 47 = 3

           5x = 3 + 47

           5x = 50

              x = 50/5

x = 10

∠1 = 4x +3 = 4*10 + 3 = 40 + 3

∠1 = 43

∠9 = 43

ΔDBE is equilateral. So all angles are equal in equilateral.

Each angel in equilateral triangle = 180÷ 3 = 60

∠4 = ∠5 = ∠6 = 60

∠3 + ∠4 = 180     {linear pair}

∠3 + 60 = 180

      ∠3 = 180 - 60

 ∠3 = 120

∠6 + ∠8 = 180    {linear pair}

60 + ∠8 = 180

      ∠8   = 180 - 60

  ∠8 = 120

In ΔABD,

∠1 + ∠2 + ∠3 = 180            {angle sum property of triangle}

43 + ∠2 + 120 = 180

     ∠2 + 163   = 180

             ∠2     = 180 - 163

∠2 = 17

In ΔBEC,

∠7 +∠8 +∠9 = 180   {angle sum property of triangle}

∠7 + 120 + 43 = 180

    ∠7   + 163 = 180

               ∠7 = 180 - 163

              ∠7 = 17