Question

1. find the measure of each angle: m∠wzn = 90° m∠uzy = m∠xzy = m∠vzx =

Explanation:

Step1: Identify vertical - angles

Vertical - angles are equal. $\angle VZW$ and $\angle YZX$ are vertical - angles, $\angle VZU$ and $\angle YZX$ are also vertical - angles.

Step2: Use the right - angle property

Since $\angle WZX = 90^{\circ}$ and $\angle VZU=25^{\circ}$.

Step3: Calculate $\angle VZW$

$\angle VZW=\angle WZX-\angle VZU$. Substitute the values: $\angle VZW = 90^{\circ}-25^{\circ}=65^{\circ}$.

Step4: Find $\angle YZX$

Because $\angle YZX$ and $\angle VZW$ are vertical - angles, $\angle YZX=\angle VZW = 65^{\circ}$.

Step5: Find $\angle UZY$

$\angle UZY$ and $\angle VZU$ are complementary (since $\angle VZW + \angle VZU=90^{\circ}$ and $\angle VZW=\angle UZY$), so $\angle UZY = 65^{\circ}$.

Step6: Find $\angle MZV$

$\angle MZV$ and $\angle UZY$ are vertical - angles, so $\angle MZV=\angle UZY = 65^{\circ}$.

Answer:

$m\angle VZW = 65^{\circ}$
$m\angle YZX = 65^{\circ}$
$m\angle UZY = 65^{\circ}$
$m\angle MZV = 65^{\circ}$