Question

algebra find the value of x for which (ell parallel m). 13. 14. 15. 16.

Explanation:

Step1: Use the property of alternate - interior angles

When \( \ell\parallel m\), alternate - interior angles are equal.
For problem 13:
\(x + 25=55\)

Step2: Solve the equation for \(x\)

Subtract 25 from both sides of the equation \(x + 25=55\).
\(x=55 - 25\)
\(x = 30\)

For problem 14:
Use the property of vertical angles and same - side interior angles. The vertical angle of \(95^{\circ}\) is \(95^{\circ}\). When \( \ell\parallel m\), same - side interior angles are supplementary.
\((2x-5)+95 = 180\)

Step2: Simplify the equation

\(2x+90=180\)

Step3: Solve for \(x\)

Subtract 90 from both sides: \(2x=180 - 90\)
\(2x=90\)
Divide both sides by 2: \(x = 45\)

For problem 15:
When \( \ell\parallel m\), corresponding angles are equal.
\(3x-33=2x - 26\)

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(3x-2x-33=2x-2x - 26\)
\(x-33=-26\)
Add 33 to both sides: \(x=-26 + 33\)
\(x = 7\)

For problem 16:
Use the property of corresponding angles and supplementary angles. The angle adjacent to \(105^{\circ}\) is \(180 - 105=75^{\circ}\). When \( \ell\parallel m\), corresponding angles are equal.
\(3x-18=75\)

Step2: Solve the equation for \(x\)

Add 18 to both sides: \(3x=75 + 18\)
\(3x=93\)
Divide both sides by 3: \(x = 31\)

Answer:

1. \(x = 30\)
2. \(x = 45\)
3. \(x = 7\)
4. \(x = 31\)