Question

Pls help. I need to solve for those 3 values and I’ll give u the Brain thing is u get it right

Answer 1

x = 11

y = 8

z = 42

Explanation:

From the given figure

∵ l
`_(1)` and l
`_(2)` 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