Question

the quadrilateral shown is a rectangle. what is m∠zwv? a 39° b 59° c 61° d 119°

Explanation:

Step1: Recall rectangle properties

In a rectangle, the diagonals are congruent and bisect each other. So, $\triangle VWX$ is an isosceles triangle with $VX = VW$.

Step2: Identify vertical - angles

The angle vertical to the given $61^{\circ}$ angle has the same measure. Let $\angle WVX=61^{\circ}$.

Step3: Use angle - sum property of a triangle

In $\triangle VWX$, since $VX = VW$, $\angle VXW=\angle VWW$. Let $\angle VWW = x$.
We know that the sum of angles in a triangle is $180^{\circ}$. So in $\triangle VWX$, $x + x+61^{\circ}=180^{\circ}$.
Combining like - terms gives $2x=180^{\circ}- 61^{\circ}=119^{\circ}$.
Then $x=\frac{119^{\circ}}{2} = 59.5^{\circ}\approx59^{\circ}$ (rounded to the nearest whole degree).

Answer:

B. $59^{\circ}$