Question

find the measures of the numbered angles in the isosceles trapezoid.

Explanation:

Step1: Recall properties of isosceles trapezoid

In an isosceles trapezoid, base angles are equal, and consecutive angles between the bases are supplementary (sum to \(180^\circ\)).

Step2: Find measure of angle 1

Since the non - parallel sides (legs) are equal, the base angles are equal. The angle given is \(33^\circ\) and angle 1 is a base angle with the same base, so \(\angle1 = 33^\circ\).

Step3: Find measure of angle 2 and angle 3

Consecutive angles between the bases are supplementary. So, \(\angle2=\angle3 = 180^\circ - 33^\circ=147^\circ\).

Answer:

\(\angle1 = 33^\circ\), \(\angle2 = 147^\circ\), \(\angle3 = 147^\circ\)