Question

1. find the measure of ∠3. 41° 49° 131°

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 (marked with single slashes), so it is an isosceles trapezoid.

Step2: Recall angle properties of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal. The given angle of \(49^{\circ}\) and the angle adjacent to \(\angle3\) (let's call it \(\angle4\)) are base - angles, so \(\angle4 = 49^{\circ}\).

Step3: Use linear - pair property

\(\angle3\) and \(\angle4\) form a linear pair. Since the sum of angles in a linear pair is \(180^{\circ}\), we have \(\angle3=180^{\circ}-\angle4\).

Step4: Calculate the measure of \(\angle3\)

Substitute \(\angle4 = 49^{\circ}\) into the formula: \(\angle3=180 - 49=131^{\circ}\).

Answer:

\(131^{\circ}\)