Question

in the figure below, l || m. find x. 130° x° 75° x =

Explanation:

Step1: Find the alternate - interior angle

Since \(l\parallel m\), the angle alternate - interior to the \(130^{\circ}\) angle is also \(130^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In the triangle formed, we know one angle is \(130^{\circ}\) and another is \(25^{\circ}\). Let the third angle be \(x\). Then \(x + 130^{\circ}+25^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\[

$$\begin{align*} x&=180^{\circ}-(130^{\circ} + 25^{\circ})\\ x&=180^{\circ}-155^{\circ}\\ x& = 25^{\circ} \end{align*}$$

\]

Answer:

\(25\)