Question

find the measures of the numbered angles in the isosceles trapezoid. m∠1 = 55°, m∠2 = 125°, m∠3 = □°

Explanation:

Step1: Use property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal. Since $\angle1$ and the given $55^{\circ}$ angle are base - angles, they are equal, so $m\angle1 = 55^{\circ}$.

Step2: Use linear - pair property

$\angle2$ and the $55^{\circ}$ angle form a linear pair. A linear pair of angles sums to $180^{\circ}$. So $m\angle2=180 - 55=125^{\circ}$.

Step3: Use base - angle equality

$\angle3$ and $\angle2$ are base - angles of the isosceles trapezoid. So $m\angle3 = 125^{\circ}$.

Answer:

$m\angle3 = 125^{\circ}$