Question

your turn

use the rhombus vwxy from example 3 to find each measure.

1. \\(m\angle vyx\\)

1. \\(m\angle xyz\\)

Explanation:

Find the value of m

Using the Rhombus Properties and Solving Linear Equations knowledge points

$$
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Find the value of n

Using the Rhombus Properties and Solving Linear Equations knowledge points

$$
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Calculate the measure of angle VYX

Using the Rhombus Properties knowledge point

$$
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Calculate the measure of angle XYZ

Using the Rhombus Properties knowledge point

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Let's verify the angle bisector property of a rhombus:
The diagonals of a rhombus bisect its angles.
Therefore, diagonal \(WY\) bisects \(\angle VYX\).
Thus, \(m\angle XYZ = m\angle VYZ = \frac{1}{2} m\angle VYX = 53.5^\circ\).

Answer:

Question 1

\(107^\circ\)

Question 2

\(53.5^\circ\)