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
