Answer:
x = 11
y = 8
z = 42
Step-by-step explanation:
From the given figure
∵ l[tex]_{1}[/tex] and l[tex]_{2}[/tex] intersected at a point
∴ ∠1 and ∠4 are vertically opposite angles
→ Vertically opposite angles are equal in measures
∴ m∠1 = m∠4
∵ m∠1 = 4(3y - 12)°
∵ m∠4 = (8y - 16)°
→ Equate their measures
∵ 4(3y - 12) = 8y - 16
∴ 4(3y) - 4(12) = 8y - 16
∴ 12y - 48 = 8y - 16
→ Subtract 8y from both sides
∵ 12y - 8y - 48 = 8y - 8y - 16
∴ 4y - 48 = -16
→ Add 48 to both sides
∴ 4y - 48 + 48 = -16 + 48
∴ 4y = 32
→ Divide both sides by 4
∴ y = 8
∵ ∠4 and ∠5 formed a pair of linear angles
→ The sum of the measures of the linear angles is 180°
∴ m∠4 + m∠5 = 180°
∵ m∠5 = (12x)°
∵ m∠4 = 8(8) - 16 = 64 - 16 = 48°
→ Add them and equate the sum by 180
∵ 48 + 12x = 180
→ Subtract 48 from both sides
∴ 48 - 48 + 12x = 180 - 48
∴ 12x = 132
→ Divide both sides by 12
∴ x = 11
∵ ∠4, ∠3, and ∠2 formed a line
∴ ∠4, ∠3, and ∠2 are linear angles
→ The sum of the measure of the linear angles is 180°
∴ m∠4 + m∠3 + m∠2 = 180°
∵ m∠4 = 48°
∵ m∠3 = 3(11) + 9 = 33 + 9 = 42°
∵ m∠2 = (2z + 6)
→ Add them and equate the sum by 180
∵ 48 + 42 + 2z + 6 = 180
→ Add the like terms in the left side
∴ 96 + 2z = 180
→ Subtract 96 from both sides
∵ 96 - 96 + 2z = 180 - 96
∴ 2z = 84
→ Divide both sides by 2
∴ z = 42
