Question

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

Explanation:

Step1: Recall property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal.

Step2: Identify angle relationship

Since the trapezoid is isosceles, $\angle1$ and the $55^{\circ}$ angle are base - angles. So $\angle1 = 55^{\circ}$.

Step3: Use linear - pair property

$\angle1$ and $\angle2$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle2=180 - m\angle1$.

Step4: Calculate $m\angle2$

Substitute $m\angle1 = 55^{\circ}$ into the formula: $m\angle2=180 - 55=125^{\circ}$.

Answer:

$m\angle1 = 55^{\circ}$, $m\angle2 = 125^{\circ}$