Question

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

Answer 1

∠1 = 43

∠2 = 17

∠3 = 120

∠4 = 60

∠5 = 60

∠6 = 60

∠7 = 17

∠8 = 120

∠9 = 43

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