Question

directions: if l || m, solve for x.
5
(9x + 2)
119°
9x+2 = 119
-2 -2
9x = 117
9x/9 = 117/9
x = 13
6.
(12x - 8)°
104°
7.
(5x + 7)
(8x - 71)
8.
(4x - 7)°
(7x - 61)°
directions: if l || m, solve for x and y.

Explanation:

Step1: Identify angle - relationship in problem 6

Since \(l\parallel m\), the angles \((12x - 8)^{\circ}\) and \(104^{\circ}\) are alternate - interior angles and are equal. So we set up the equation \(12x-8 = 104\).

Step2: Solve the equation for \(x\) in problem 6

Add 8 to both sides of the equation: \(12x-8 + 8=104 + 8\), which simplifies to \(12x=112\). Then divide both sides by 12: \(x=\frac{112}{12}=\frac{28}{3}\approx9.33\).

Step3: Identify angle - relationship in problem 7

Since \(l\parallel m\), the angles \((5x + 7)^{\circ}\) and \((8x-71)^{\circ}\) are corresponding angles and are equal. So we set up the equation \(5x + 7=8x-71\).

Step4: Solve the equation for \(x\) in problem 7

Subtract \(5x\) from both sides: \(5x + 7-5x=8x-71-5x\), which gives \(7 = 3x-71\). Then add 71 to both sides: \(7+71=3x-71 + 71\), so \(78 = 3x\). Divide both sides by 3: \(x = 26\).

Step5: Identify angle - relationship in problem 8

Since \(l\parallel m\), the angles \((4x-7)^{\circ}\) and \((7x - 61)^{\circ}\) are alternate - exterior angles and are equal. So we set up the equation \(4x-7=7x-61\).

Step6: Solve the equation for \(x\) in problem 8

Subtract \(4x\) from both sides: \(4x-7-4x=7x-61-4x\), which gives \(-7 = 3x-61\). Add 61 to both sides: \(-7 + 61=3x-61+61\), so \(54 = 3x\). Divide both sides by 3: \(x = 18\).

Answer:

Problem 6: \(x=\frac{28}{3}\)
Problem 7: \(x = 26\)
Problem 8: \(x = 18\)