Question

12 120° x°

Explanation:

Step1: Find the interior angle of the first triangle

The angle adjacent to \(120^{\circ}\) is \(180 - 120=60^{\circ}\) (supplementary angles). Since the two sides of the first triangle are equal (marked with one tick), it is an isosceles triangle. The other two angles of the isosceles triangle are equal. Let each of them be \(y\). Using the angle - sum property of a triangle (\(y + y+60 = 180\)), we get \(2y=120\), so \(y = 60^{\circ}\).

Step2: Use the properties of parallel lines and congruent triangles

The two segments (marked with two ticks) are equal. The lines (formed by the triangles) are related by the properties of parallel lines and congruent triangles (by SAS - Side - Angle - Side congruence, since we have two sides equal and the included angle equal from the previous step). The angle \(x\) is equal to the angle we found in the first triangle.

Answer:

\(x = 60\)