Question

finding an angle measure given a triangle and parallel lines
in the figure below, ( l parallel m ). find ( x ).
( x = )

Explanation:

Step1: Find the alternate interior angle

Since \(l\parallel m\), the angle adjacent to \(125^{\circ}\) on line \(l\) is \(180 - 125=55^{\circ}\) (linear - pair angles).

Step2: Use the triangle - angle sum property

In the triangle, we know that the sum of angles in a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(55^{\circ}\), \(65^{\circ}\), and \(x^{\circ}\). Then \(55 + 65+x=180\).
Simplify the left - hand side: \(120 + x=180\).
Subtract 120 from both sides: \(x=180 - 120\).

Answer:

\(x = 60\)