instructions: find the measurement of the angle indicated for the following trapezoid. m∠ =

Explanation:

Step1: Recall trapezoid angle - sum property

The sum of the interior angles of a trapezoid (a quadrilateral) is $(4 - 2)\times180^{\circ}=360^{\circ}$. Also, since $WX = YZ$, this is an isosceles trapezoid, and $\angle W=\angle Z = 46^{\circ}$, and $\angle X=\angle Y$.

Step2: Set up an equation

Let $m\angle X = m\angle Y=x$. Then $m\angle W + m\angle X+m\angle Y + m\angle Z=360^{\circ}$. Substituting the known values, we get $46^{\circ}+x + x+46^{\circ}=360^{\circ}$.

Step3: Simplify the equation

Combining like - terms, $92^{\circ}+2x = 360^{\circ}$.

Step4: Solve for $x$

Subtract $92^{\circ}$ from both sides: $2x=360^{\circ}-92^{\circ}=268^{\circ}$. Then divide both sides by 2: $x = 134^{\circ}$.

Answer:

$134$