Question

in the figure below, l || m. find x.

Explanation:

Step1: Find the alternate - interior angle

Since \(l\parallel m\), the angle alternate - interior to the \(141^{\circ}\) angle is also \(141^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In the triangle, we know one angle is \(93^{\circ}\) and another is \(141^{\circ}\) (the alternate - interior angle). Let the third angle be \(x\). So, \(x+93^{\circ}+(180 - 141)^{\circ}=180^{\circ}\). First, simplify \(180 - 141=39^{\circ}\). Then the equation becomes \(x + 93^{\circ}+39^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Combine like terms: \(x+(93 + 39)^{\circ}=180^{\circ}\), so \(x + 132^{\circ}=180^{\circ}\). Subtract \(132^{\circ}\) from both sides: \(x=180^{\circ}-132^{\circ}\).

Answer:

\(48\)