Quadrilateral ZYXW is a rhombus. If m∠VWZ= 39°𝑚∠𝑉𝑊𝑍= 39° , find  m∠VZW𝑚∠𝑉𝑍𝑊 .

In a rhombus, opposite angles are equal and adjacent angles are supplementary.

Given that m∠VWZ = 39°, we know that its adjacent angle, m∠VZW, is supplementary to it.

The sum of supplementary angles is 180°.

Therefore, to find m∠VZW, we subtract m∠VWZ from 180°.

So, m∠VZW = 180° - 39° = 141°.

In a rhombus, the diagonals bisect the angles. Therefore, if the measure of angle VWZ is 39 degrees, then the measure of angle VZW, which is bisected by the diagonal, will be half of 39 degrees.

Step 1: Identify the given angle. In this case, it's ∠VWZ which is 39°. Step 2: Since diagonals in a rhombus bisect the angles, the measure of ∠VZW will be half of the measure of ∠VWZ. Step 3: Calculate the measure of ∠VZW by dividing the measure of ∠VWZ by 2.

So, m∠VZW = m∠VWZ / 2 = 39° / 2 = 19.5°

Therefore, the measure of angle VZW is 19.5 degrees.

In a rhombus, the diagonals bisect the angles. Therefore, if the measure of angle VWZ is 39 degrees, then the measure of angle VZW will be half of that, which is 39/2 = 19.5 degrees.