Question

1. find the measure of ∠2

Explanation:

Step1: Identify the trapezoid type

The trapezoid has one - pair of parallel sides (indicated by the red arrows) and non - parallel sides are equal (indicated by the single slashes on the non - parallel sides), so it is an isosceles trapezoid.

Step2: Recall angle property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal. The angle adjacent to the given \(49^{\circ}\) angle and \(\angle2\) are supplementary (since the two parallel lines are cut by a transversal). Let the given angle be \(\angle4 = 49^{\circ}\). The sum of adjacent angles along a non - parallel side of a trapezoid (for parallel bases) is \(180^{\circ}\).

Step3: Calculate the measure of \(\angle2\)

We know that \(\angle2+\angle4 = 180^{\circ}\). Substituting \(\angle4 = 49^{\circ}\), we get \(\angle2=180^{\circ}- 49^{\circ}=131^{\circ}\).

Answer:

\(131^{\circ}\)