Fill in the blank question.Quadrilateral ZYXW is a rhombus. If m∠VWZ= 39°𝑚∠𝑉𝑊𝑍= 39° , find  m∠VZW𝑚∠𝑉𝑍𝑊 .

1. Break Down the Problem

We know that quadrilateral ZYXW is a rhombus. In a rhombus, the opposite angles are equal, and the adjacent angles are supplementary (sum to 180°). We want to find the measure of angle $m\angle VZW$ given that $m\angle VWZ = 39°$.

2. Relevant Concepts

• The sum of the angles in a quadrilateral is 360°.
• In a rhombus, adjacent angles are supplementary: $m\angle VZW + m\angle VWZ = 180°$.

3. Analysis and Detail

From the given information:

• Knowing $m\angle VWZ = 39°$,
• We can find $m\angle VZW$ using the supplementary angle property:

$m\angle VZW + m\angle VWZ = 180°$

Substituting the known value: $m\angle VZW + 39° = 180°$

Now, we solve for $m\angle VZW$: $m\angle VZW = 180° - 39°$

4. Verify and Summarize

Performing the calculation: $m\angle VZW = 180° - 39° = 141°$

Final Answer

The measure of angle $m\angle VZW$ is $141°$.