Answer:
∠1 = 35 ; ∠2 = 65 ; ∠3 = 29 ; ∠4 = 115
∠5 = 65 ; ∠6 = 36 ; ∠7 = 144
Step-by-step explanation:
∠4 = 115 {Vertically opposite angles}
∠5 + 115 = 180 {linear pair}
∠5 = 180 - 115
∠5 = 65
∠2 = ∠5 {Vertically opposite angles}
∠2 = 65
∠1 + 80 +∠2 = 180 {Angle sum property of triangle}
∠1 + 80 + 65=180
∠1 + 145 = 180
∠1 = 180 - 145
∠1 = 35
∠5 + ∠7 + 90 + 61 = 360 {angle sum property of quadrilateral}
65 + ∠ 7 + 90 + 61 = 360
∠7 + 216 = 360
∠7 = 360 - 216
∠7 = 144
∠6 + ∠ 7 = 180 {linear pair}
∠6 + 144 = 180
∠6 = 180 - 144
∠6 = 36
∠3 + ∠4 +∠ 6 = 180 {angle sum property of triangle}
∠3 + 115 + 36 = 180
∠3 + 151 = 180
∠3 = 180 - 151
∠3 = 29
