Answer:
Step-by-step explanation:
1) ∠2 = 88 {Vertically opposite angles}
∠2 +∠1 = 180 {Linear pair}
88 + ∠1 = 180
∠1 = 180 - 88
∠1 = 92°
∠3 = ∠1 {Vertically opposite angles}
∠3 = 92
Answer: ∠1 = ∠3 = 92° and ∠2 = 88°
2) AB ⊥ CD
∠BOD = 90
∠BOT + ∠TOD = ∠BOD
3x + 36 + 5x - 4 = 90
3x + 5x + 36 - 4 = 90 {Combine like terms}
8x + 32 = 90 {Subtract 32 form both sides}
8x = 90 - 32
8x = 58
x = 58/8
x = 7.25
3) BD is angle bisector of ∠ABC. So,
∠ABD = ∠DBC
7x - 16 = 4x - 1
Add 16 to both sides
7x = 4x - 1 + 16
7x = 4x + 15
Subtract 4x from both sides
7x - 4x = 15
3x = 15
Divide both sides by 3
x = 15/3
x = 5
4)9x + 22 = x + 46 {Vertically opposite angles}
Subtract 22 form both sides
9x = x + 46 - 22
9x = x + 24
Subtract 'x' form both sides
9x - x = 24
8x = 24
Divide both sides by 8
x = 24/8
x = 3
x + 46 + 2y + 7 = 180 {linear pair}
Plugin x = 3,
3 + 46 + 2y + 7 = 180
2y + 56 = 180
2y = 180 - 56
2y = 124
y = 124/2
y = 62
