Question

introduction to quadrilaterals (thurs 1/8)
if wxyz is an isosceles trapezoid, find ( mangle w ).
( (9x + 15)^circ ) at angle x, ( (14x - 50)^circ ) at angle y. the measure of angle w is blank.

Explanation:

Step1: Recall properties of isosceles trapezoid

In an isosceles trapezoid, base angles are equal, and consecutive angles between the bases are supplementary. Also, the non - base angles (the angles adjacent to the legs) are equal. Here, $\angle X$ and $\angle Y$ are the angles at the top base $XY$. In an isosceles trapezoid, the base angles are equal, so we set the expressions for $\angle X$ and $\angle Y$ equal:
$9x + 15=14x - 50$

Step2: Solve for $x$

Subtract $9x$ from both sides:
$15 = 14x-9x - 50$
$15=5x - 50$
Add 50 to both sides:
$15 + 50=5x$
$65 = 5x$
Divide both sides by 5:
$x=\frac{65}{5}=13$

Step3: Find the measure of $\angle X$ (or $\angle Y$)

Substitute $x = 13$ into the expression for $\angle X$:
$\angle X=9\times13 + 15=117+15 = 132^{\circ}$

Step4: Find the measure of $\angle W$

Since $\angle W$ and $\angle X$ are consecutive angles between the bases ( $WZ$ and $XY$ are the two bases), they are supplementary. So $m\angle W+ m\angle X = 180^{\circ}$
$m\angle W=180^{\circ}-m\angle X$
Substitute $m\angle X = 132^{\circ}$:
$m\angle W=180 - 132=48^{\circ}$

Answer:

$48^{\circ}$