Question

1. find the value of x for which ℓ || m.

a)
ℓ
m
55°
(x + 25)°
b)
ℓ
m
95°
(2x - 5)°

Explanation:

Part (a)

Step1: Identify the angle relationship

For lines \(\ell\) and \(m\) to be parallel, the corresponding angles should be equal. The \(55^\circ\) angle and \((x + 25)^\circ\) angle are corresponding angles. So we set up the equation:
\(x + 25 = 55\)

Step2: Solve for \(x\)

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

Part (b)

Step1: Identify the angle relationship

For lines \(\ell\) and \(m\) to be parallel, the alternate interior angles should be equal. The \(95^\circ\) angle and \((2x - 5)^\circ\) angle are alternate interior angles. So we set up the equation:
\(2x - 5 = 95\)

Step2: Solve for \(x\)

Add 5 to both sides:
\(2x = 95 + 5\)
\(2x = 100\)
Divide both sides by 2:
\(x = \frac{100}{2}\)
\(x = 50\)

Answer:

s:
a) \(x = 30\)
b) \(x = 50\)