Question

directions: if l || m, find the value of each missing variable(s). 3. (9x + 2)° 119° 4. (12x - 8)° 104° 5. (5x + 7)° (8x - 71)° 6. (2x - 7)° (29 - x)°

Explanation:

Step1: Identify angle - relationship (for 5)

When \(l\parallel m\), the given angles \((5x + 7)^{\circ}\) and \((8x-71)^{\circ}\) are alternate - interior angles, so they are equal.
\[5x + 7=8x - 71\]

Step2: Solve the equation for \(x\) (for 5)

Subtract \(5x\) from both sides:
\[7 = 3x-71\]
Add 71 to both sides:
\[7+71 = 3x\]
\[78 = 3x\]
Divide both sides by 3:
\[x = 26\]

Step1: Identify angle - relationship (for 3)

When \(l\parallel m\), the angle \((9x + 2)^{\circ}\) and \(119^{\circ}\) are corresponding angles, so \(9x+2 = 119\).

Step2: Solve the equation for \(x\) (for 3)

Subtract 2 from both sides:
\[9x=119 - 2\]
\[9x = 117\]
Divide both sides by 9:
\[x = 13\]

Step1: Identify angle - relationship (for 4)

When \(l\parallel m\), the angle \((12x-8)^{\circ}\) and \(104^{\circ}\) are corresponding angles, so \(12x-8 = 104\).

Step2: Solve the equation for \(x\) (for 4)

Add 8 to both sides:
\[12x=104 + 8\]
\[12x = 112\]
Divide both sides by 12:
\[x=\frac{112}{12}=\frac{28}{3}\]

Step1: Identify angle - relationship (for 6)

When \(l\parallel m\), the angles \((2x - 7)^{\circ}\) and \((29 - x)^{\circ}\) are same - side interior angles, so \((2x - 7)+(29 - x)=180\).

Step2: Simplify the left - hand side of the equation (for 6)

\[2x-7 + 29 - x=x + 22\]
So, \(x + 22=180\).

Step3: Solve the equation for \(x\) (for 6)

Subtract 22 from both sides:
\[x=180 - 22\]
\[x = 158\]

Answer:

For 3: \(x = 13\)
For 4: \(x=\frac{28}{3}\)
For 5: \(x = 26\)
For 6: \(x = 158\)